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

## Example Questions

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### Example Question #1 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear 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 straight line, the general algebraic form of the function is,

where

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

Therefore the general form of the function looks like,

The -intercept is three.

### Example Question #2 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear 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 straight line, the general algebraic form of the function is,

where

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

Therefore the general form of the function looks like,

The -intercept is negative one.

### Example Question #3 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear 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 straight line, the general algebraic form of the function is,

where

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

Therefore the general form of the function looks like,

The -intercept is five.

### Example Question #4 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear 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 straight line, the general algebraic form of the function is,

where

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

Therefore the general form of the function looks like,

The -intercept is negative two.

### Example Question #5 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear 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 straight line, the general algebraic form of the function is,

where

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

Therefore the general form of the function looks like,

The -intercept is four.

### Example Question #6 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

Explanation:

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear 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 straight line, the general algebraic form of the function is,

where

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

Therefore the general form of the function looks like,

The -intercept is negative two.

### Example Question #7 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

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,

where

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

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

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at  which means the -intercept is one.

The -intercept is one.

### Example Question #8 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

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,

where

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

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

For the function above, the vertex is also the maximum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at  which means the -intercept is three.

The -intercept is three.

### Example Question #9 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

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,

where

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

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

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at  which means the -intercept is two.

The -intercept is two.

### Example Question #10 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

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,

where

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

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

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at  which means the -intercept is zero.