Advantages and Disadvantages of the different forms of a quadratic function

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!

edited Mar 6 at 20:10

Bernard

117k637109

asked Mar 6 at 20:02

Rawnaa F

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

add a comment |

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!

edited Mar 6 at 20:10

Bernard

117k637109

asked Mar 6 at 20:02

Rawnaa F

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

add a comment |

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!

edited Mar 6 at 20:10

Bernard

117k637109

asked Mar 6 at 20:02

Rawnaa F

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

edited Mar 6 at 20:10

Bernard

117k637109

asked Mar 6 at 20:02

Rawnaa F

edited Mar 6 at 20:10

Bernard

117k637109

asked Mar 6 at 20:02

Rawnaa F

edited Mar 6 at 20:10

Bernard

117k637109

edited Mar 6 at 20:10

Bernard

117k637109

edited Mar 6 at 20:10

Bernard

117k637109

asked Mar 6 at 20:02

Rawnaa F

asked Mar 6 at 20:02

Rawnaa F

asked Mar 6 at 20:02

Rawnaa F

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

add a comment |

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

add a comment |

2 Answers
2

active

oldest

votes

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.

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

answered Mar 6 at 20:12

Jesse Meng

1,150217

add a comment |

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

edited Mar 6 at 22:25

answered Mar 6 at 20:16

user535339

add a comment |

Your Answer

StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\$","\$"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});

}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2679787%2fadvantages-and-disadvantages-of-the-different-forms-of-a-quadratic-function%23new-answer', 'question_page');
}
);

Post as a guest

Name

Required, but never shown

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
0
down vote

Factorized Form

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

Conclusion

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

answered Mar 6 at 20:12

Jesse Meng

1,150217

add a comment |

up vote
0
down vote

Factorized Form

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

Conclusion

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

answered Mar 6 at 20:12

Jesse Meng

1,150217

add a comment |

up vote
0
down vote

Factorized Form

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

Conclusion

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

answered Mar 6 at 20:12

Jesse Meng

1,150217

Factorized Form

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

Conclusion

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

answered Mar 6 at 20:12

Jesse Meng

1,150217

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

edited Mar 6 at 20:22

Mehrdad Zandigohar

1,495216

answered Mar 6 at 20:12

Jesse Meng

1,150217

answered Mar 6 at 20:12

Jesse Meng

1,150217

answered Mar 6 at 20:12

Jesse Meng

1,150217

add a comment |

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

edited Mar 6 at 22:25

answered Mar 6 at 20:16

user535339

add a comment |

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

edited Mar 6 at 22:25

answered Mar 6 at 20:16

user535339

add a comment |

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

edited Mar 6 at 22:25

answered Mar 6 at 20:16

user535339

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

edited Mar 6 at 22:25

answered Mar 6 at 20:16

user535339

edited Mar 6 at 22:25

answered Mar 6 at 20:16

user535339

answered Mar 6 at 20:16

user535339

answered Mar 6 at 20:16

user535339

add a comment |

draft saved

draft discarded

Thanks for contributing an answer to Mathematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

To learn more, see our tips on writing great answers.

Some of your past answers have not been well-received, and you're in danger of being blocked from answering.

Please pay close attention to the following guidance:

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience.

To learn more, see our tips on writing great answers.

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Name

Required, but never shown

Name

Required, but never shown

This page is only for reference, If you need detailed information, please check here

搜尋此網誌

Jtdylktuy