### All Common Core: High School - Functions Resources

## Example Questions

### Example Question #81 : High School: Functions

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

**Possible Answers:**

**Correct answer:**

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 parabola is shifted to the right therefore the -intercept of the graph is not at the vertex.

Therefore the -intercept lies at the point which means the -intercept is four.

Step 3: Answer the question.

The -intercept is four.

### Example Question #82 : Interpreting Functions

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

**Possible Answers:**

**Correct answer:**

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 parabola is shifted to the right therefore the -intercept of the graph is not at the vertex.

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

Step 3: Answer the question.

The -intercept is one.

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