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Common Core: High School - Functions : Graph Linear and Quadratic Functions: CCSS.Math.Content.HSF-IF.C.7a

Study concepts, example questions & explanations for Common Core: High School - Functions

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All Common Core: High School - Functions Resources

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Example Questions

Example Question #81 : High School: Functions

Screen shot 2016 01 23 at 7.50.16 am

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

$\textup{y-intercept}=4$

$\textup{y-intercept}=2$

$\textup{y-intercept}=1$

$\textup{y-intercept}=0$

$\textup{y-intercept}=8$

Correct answer:

$\textup{y-intercept}=4$

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

y=ax^2+bx+c

where

$\\a=\textup{The width/pitch of the parabola} \\b=\textup{Relates to the vertex}=\frac{-b}{2a} \\c=\textup{Vertical Shift}$

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if 0<a<1 then the width of the parabola is wider; if a>1 then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

Screen shot 2016 01 23 at 7.50.16 am

For the function above, the parabola is shifted to the right therefore the -intercept of the graph is not at the vertex.

Therefore the -intercept lies at the point (0,4) which means the -intercept is four.

Step 3: Answer the question.

The -intercept is four.

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Example Question #82 : High School: Functions

Screen shot 2016 01 23 at 7.50.54 am

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

$\textup{y-intercept}=-1$

$\textup{y-intercept}=2$

$\textup{y-intercept}=0$

$\textup{y-intercept}=4$

$\textup{y-intercept}=1$

Correct answer:

$\textup{y-intercept}=1$

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

y=ax^2+bx+c

where

$\\a=\textup{The width/pitch of the parabola} \\b=\textup{Relates to the vertex}=\frac{-b}{2a} \\c=\textup{Vertical Shift}$

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if 0<a<1 then the width of the parabola is wider; if a>1 then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

Screen shot 2016 01 23 at 7.50.54 am

For the function above, the parabola is shifted to the right therefore the -intercept of the graph is not at the vertex.

Therefore the -intercept lies at the point (0,1) which means the -intercept is one.

Step 3: Answer the question.

The -intercept is one.

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All Common Core: High School - Functions Resources

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Common Core: High School - Functions : Graph Linear and Quadratic Functions: CCSS.Math.Content.HSF-IF.C.7a

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #81 : High School: Functions

Example Question #82 : High School: Functions

All Common Core: High School - Functions Resources

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