Advantages and Disadvantages of the different forms of a quadratic function











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My question is when sketching a graph what are the advantages and disadvantages for the following:



i. Standard form



ii. Factorised form



iii. Vertex form



Many thanks!






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  • What do you mean by advantages and disadvantages? You mean if one is easier for sketching although it may be harder to formulate?
    – Mehrdad Zandigohar
    Mar 6 at 20:16










  • Yes, i mean when someone sees the equation of the three different forms but with the same graph what are the advantages of using one graph instead of the other.
    – Rawnaa F
    Mar 6 at 20:21















up vote
0
down vote

favorite












My question is when sketching a graph what are the advantages and disadvantages for the following:



i. Standard form



ii. Factorised form



iii. Vertex form



Many thanks!






quadratics







share|cite|improve this question
























  • What do you mean by advantages and disadvantages? You mean if one is easier for sketching although it may be harder to formulate?
    – Mehrdad Zandigohar
    Mar 6 at 20:16










  • Yes, i mean when someone sees the equation of the three different forms but with the same graph what are the advantages of using one graph instead of the other.
    – Rawnaa F
    Mar 6 at 20:21













up vote
0
down vote

favorite









up vote
0
down vote

favorite











My question is when sketching a graph what are the advantages and disadvantages for the following:



i. Standard form



ii. Factorised form



iii. Vertex form



Many thanks!






quadratics







share|cite|improve this question















My question is when sketching a graph what are the advantages and disadvantages for the following:



i. Standard form



ii. Factorised form



iii. Vertex form



Many thanks!






quadratics




quadratics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 6 at 20:10









Bernard

117k637109




117k637109










asked Mar 6 at 20:02









Rawnaa F

12




12












  • What do you mean by advantages and disadvantages? You mean if one is easier for sketching although it may be harder to formulate?
    – Mehrdad Zandigohar
    Mar 6 at 20:16










  • Yes, i mean when someone sees the equation of the three different forms but with the same graph what are the advantages of using one graph instead of the other.
    – Rawnaa F
    Mar 6 at 20:21


















  • What do you mean by advantages and disadvantages? You mean if one is easier for sketching although it may be harder to formulate?
    – Mehrdad Zandigohar
    Mar 6 at 20:16










  • Yes, i mean when someone sees the equation of the three different forms but with the same graph what are the advantages of using one graph instead of the other.
    – Rawnaa F
    Mar 6 at 20:21
















What do you mean by advantages and disadvantages? You mean if one is easier for sketching although it may be harder to formulate?
– Mehrdad Zandigohar
Mar 6 at 20:16




What do you mean by advantages and disadvantages? You mean if one is easier for sketching although it may be harder to formulate?
– Mehrdad Zandigohar
Mar 6 at 20:16












Yes, i mean when someone sees the equation of the three different forms but with the same graph what are the advantages of using one graph instead of the other.
– Rawnaa F
Mar 6 at 20:21




Yes, i mean when someone sees the equation of the three different forms but with the same graph what are the advantages of using one graph instead of the other.
– Rawnaa F
Mar 6 at 20:21










2 Answers
2






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0
down vote














  • Factorized Form


With factorized form, you can easily see the two roots of the quadratic, which means you can sketch the shape of the graph easily by plotting the two zeros. Then draw an upward curve or downward curve depending on the sign on the $x^2$ term. The x-coordinate of the vertex lies exactly half way in between the roots. And hence you can determine the y-coordinate by substitution.




  • Vertex Form


With vertex form, you can easily graph the vertex point and the general shape of the quadratic given the leading coefficient. However, you cannot determine the zeros immediately.




  • Standard Form


For standard form, you will only know whether the quadratic is concave up or down and factorized/vertex forms are better in terms of sketching a graph. However, there are other advantages involved with the standard form, such as the easiness of computing the derivative and then using it to find the vertex.




  • Conclusion


So, from the analysis, factorized form seems to be the best choice for graphing, as the roots are trivial to find and vertex can be computed easily. Whereas the vertex form requires a little more effort to solve for the zeroes of the quadratic.






share|cite|improve this answer






























    up vote
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    down vote













    Standard form:



    $f(x)=ax^2+bx+c$




    • can easily notice $c$ is the $y$ intercept

    • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

    • if $|a|>1$, the graph is vertically stretched

    • if $0<|a|<1$, the graph is vertically shrunk

    • if $a>0$, the parabola faces upwards

    • if $a<0$, the parabola faces downwards

    • is easier to differentiate/integrate


    Factorized form:



    $f(x)=a(x-p)(x-q)$




    • $x=p$ and $x=q$ are roots or $y$ intercepts of the parabola.

    • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

    • if $|a|>1$, the graph is vertically stretched

    • if $0<|a|<1$, the graph is vertically shrunk

    • if $a>0$, the parabola faces upwards

    • if $a<0$, the parabola faces downwards


    Vertex Form:



    $f(x)=a(x-h)^2+k$




    • $x=h$ is the line of symmetry

    • $(h,k)$ is the minimum/maximum point of the parabola, also known as the vertex

    • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

    • if $|a|>1$, the graph is vertically stretched

    • if $0<|a|<1$, the graph is vertically shrunk

    • if $a>0$, the parabola faces upwards

    • if $a<0$, the parabola faces downwards






    share|cite|improve this answer























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      2 Answers
      2






      active

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      2 Answers
      2






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      active

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      up vote
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      • Factorized Form


      With factorized form, you can easily see the two roots of the quadratic, which means you can sketch the shape of the graph easily by plotting the two zeros. Then draw an upward curve or downward curve depending on the sign on the $x^2$ term. The x-coordinate of the vertex lies exactly half way in between the roots. And hence you can determine the y-coordinate by substitution.




      • Vertex Form


      With vertex form, you can easily graph the vertex point and the general shape of the quadratic given the leading coefficient. However, you cannot determine the zeros immediately.




      • Standard Form


      For standard form, you will only know whether the quadratic is concave up or down and factorized/vertex forms are better in terms of sketching a graph. However, there are other advantages involved with the standard form, such as the easiness of computing the derivative and then using it to find the vertex.




      • Conclusion


      So, from the analysis, factorized form seems to be the best choice for graphing, as the roots are trivial to find and vertex can be computed easily. Whereas the vertex form requires a little more effort to solve for the zeroes of the quadratic.






      share|cite|improve this answer



























        up vote
        0
        down vote














        • Factorized Form


        With factorized form, you can easily see the two roots of the quadratic, which means you can sketch the shape of the graph easily by plotting the two zeros. Then draw an upward curve or downward curve depending on the sign on the $x^2$ term. The x-coordinate of the vertex lies exactly half way in between the roots. And hence you can determine the y-coordinate by substitution.




        • Vertex Form


        With vertex form, you can easily graph the vertex point and the general shape of the quadratic given the leading coefficient. However, you cannot determine the zeros immediately.




        • Standard Form


        For standard form, you will only know whether the quadratic is concave up or down and factorized/vertex forms are better in terms of sketching a graph. However, there are other advantages involved with the standard form, such as the easiness of computing the derivative and then using it to find the vertex.




        • Conclusion


        So, from the analysis, factorized form seems to be the best choice for graphing, as the roots are trivial to find and vertex can be computed easily. Whereas the vertex form requires a little more effort to solve for the zeroes of the quadratic.






        share|cite|improve this answer

























          up vote
          0
          down vote










          up vote
          0
          down vote










          • Factorized Form


          With factorized form, you can easily see the two roots of the quadratic, which means you can sketch the shape of the graph easily by plotting the two zeros. Then draw an upward curve or downward curve depending on the sign on the $x^2$ term. The x-coordinate of the vertex lies exactly half way in between the roots. And hence you can determine the y-coordinate by substitution.




          • Vertex Form


          With vertex form, you can easily graph the vertex point and the general shape of the quadratic given the leading coefficient. However, you cannot determine the zeros immediately.




          • Standard Form


          For standard form, you will only know whether the quadratic is concave up or down and factorized/vertex forms are better in terms of sketching a graph. However, there are other advantages involved with the standard form, such as the easiness of computing the derivative and then using it to find the vertex.




          • Conclusion


          So, from the analysis, factorized form seems to be the best choice for graphing, as the roots are trivial to find and vertex can be computed easily. Whereas the vertex form requires a little more effort to solve for the zeroes of the quadratic.






          share|cite|improve this answer















          • Factorized Form


          With factorized form, you can easily see the two roots of the quadratic, which means you can sketch the shape of the graph easily by plotting the two zeros. Then draw an upward curve or downward curve depending on the sign on the $x^2$ term. The x-coordinate of the vertex lies exactly half way in between the roots. And hence you can determine the y-coordinate by substitution.




          • Vertex Form


          With vertex form, you can easily graph the vertex point and the general shape of the quadratic given the leading coefficient. However, you cannot determine the zeros immediately.




          • Standard Form


          For standard form, you will only know whether the quadratic is concave up or down and factorized/vertex forms are better in terms of sketching a graph. However, there are other advantages involved with the standard form, such as the easiness of computing the derivative and then using it to find the vertex.




          • Conclusion


          So, from the analysis, factorized form seems to be the best choice for graphing, as the roots are trivial to find and vertex can be computed easily. Whereas the vertex form requires a little more effort to solve for the zeroes of the quadratic.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Mar 6 at 20:22









          Mehrdad Zandigohar

          1,495216




          1,495216










          answered Mar 6 at 20:12









          Jesse Meng

          1,150217




          1,150217






















              up vote
              0
              down vote













              Standard form:



              $f(x)=ax^2+bx+c$




              • can easily notice $c$ is the $y$ intercept

              • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

              • if $|a|>1$, the graph is vertically stretched

              • if $0<|a|<1$, the graph is vertically shrunk

              • if $a>0$, the parabola faces upwards

              • if $a<0$, the parabola faces downwards

              • is easier to differentiate/integrate


              Factorized form:



              $f(x)=a(x-p)(x-q)$




              • $x=p$ and $x=q$ are roots or $y$ intercepts of the parabola.

              • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

              • if $|a|>1$, the graph is vertically stretched

              • if $0<|a|<1$, the graph is vertically shrunk

              • if $a>0$, the parabola faces upwards

              • if $a<0$, the parabola faces downwards


              Vertex Form:



              $f(x)=a(x-h)^2+k$




              • $x=h$ is the line of symmetry

              • $(h,k)$ is the minimum/maximum point of the parabola, also known as the vertex

              • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

              • if $|a|>1$, the graph is vertically stretched

              • if $0<|a|<1$, the graph is vertically shrunk

              • if $a>0$, the parabola faces upwards

              • if $a<0$, the parabola faces downwards






              share|cite|improve this answer



























                up vote
                0
                down vote













                Standard form:



                $f(x)=ax^2+bx+c$




                • can easily notice $c$ is the $y$ intercept

                • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                • if $|a|>1$, the graph is vertically stretched

                • if $0<|a|<1$, the graph is vertically shrunk

                • if $a>0$, the parabola faces upwards

                • if $a<0$, the parabola faces downwards

                • is easier to differentiate/integrate


                Factorized form:



                $f(x)=a(x-p)(x-q)$




                • $x=p$ and $x=q$ are roots or $y$ intercepts of the parabola.

                • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                • if $|a|>1$, the graph is vertically stretched

                • if $0<|a|<1$, the graph is vertically shrunk

                • if $a>0$, the parabola faces upwards

                • if $a<0$, the parabola faces downwards


                Vertex Form:



                $f(x)=a(x-h)^2+k$




                • $x=h$ is the line of symmetry

                • $(h,k)$ is the minimum/maximum point of the parabola, also known as the vertex

                • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                • if $|a|>1$, the graph is vertically stretched

                • if $0<|a|<1$, the graph is vertically shrunk

                • if $a>0$, the parabola faces upwards

                • if $a<0$, the parabola faces downwards






                share|cite|improve this answer

























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Standard form:



                  $f(x)=ax^2+bx+c$




                  • can easily notice $c$ is the $y$ intercept

                  • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                  • if $|a|>1$, the graph is vertically stretched

                  • if $0<|a|<1$, the graph is vertically shrunk

                  • if $a>0$, the parabola faces upwards

                  • if $a<0$, the parabola faces downwards

                  • is easier to differentiate/integrate


                  Factorized form:



                  $f(x)=a(x-p)(x-q)$




                  • $x=p$ and $x=q$ are roots or $y$ intercepts of the parabola.

                  • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                  • if $|a|>1$, the graph is vertically stretched

                  • if $0<|a|<1$, the graph is vertically shrunk

                  • if $a>0$, the parabola faces upwards

                  • if $a<0$, the parabola faces downwards


                  Vertex Form:



                  $f(x)=a(x-h)^2+k$




                  • $x=h$ is the line of symmetry

                  • $(h,k)$ is the minimum/maximum point of the parabola, also known as the vertex

                  • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                  • if $|a|>1$, the graph is vertically stretched

                  • if $0<|a|<1$, the graph is vertically shrunk

                  • if $a>0$, the parabola faces upwards

                  • if $a<0$, the parabola faces downwards






                  share|cite|improve this answer














                  Standard form:



                  $f(x)=ax^2+bx+c$




                  • can easily notice $c$ is the $y$ intercept

                  • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                  • if $|a|>1$, the graph is vertically stretched

                  • if $0<|a|<1$, the graph is vertically shrunk

                  • if $a>0$, the parabola faces upwards

                  • if $a<0$, the parabola faces downwards

                  • is easier to differentiate/integrate


                  Factorized form:



                  $f(x)=a(x-p)(x-q)$




                  • $x=p$ and $x=q$ are roots or $y$ intercepts of the parabola.

                  • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                  • if $|a|>1$, the graph is vertically stretched

                  • if $0<|a|<1$, the graph is vertically shrunk

                  • if $a>0$, the parabola faces upwards

                  • if $a<0$, the parabola faces downwards


                  Vertex Form:



                  $f(x)=a(x-h)^2+k$




                  • $x=h$ is the line of symmetry

                  • $(h,k)$ is the minimum/maximum point of the parabola, also known as the vertex

                  • $a$ tells you the vertical stretch/shrink of the graph, and the direction the parabola is facing

                  • if $|a|>1$, the graph is vertically stretched

                  • if $0<|a|<1$, the graph is vertically shrunk

                  • if $a>0$, the parabola faces upwards

                  • if $a<0$, the parabola faces downwards







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Mar 6 at 22:25

























                  answered Mar 6 at 20:16







                  user535339





































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