### All Common Core: 8th Grade Math Resources

## Example Questions

### Example Question #1 : How To Graph A Quadratic Function

Which is the graph of ?

**Possible Answers:**

**Correct answer:**

Think of the graph of :

Constants within the parentheses will shift the parabola to the left and right, while terms outside of the parentheses will shift it vertically.

In our equation, there is a -2 term outside the parentheses. This will shift the graph down by 2 units.

The graph of will look like this:

There is also a constant within the parentheses, –1. This will shift the graph to the right by 1 unit.

Therefore will generate a graph like this:

### Example Question #1 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Which of the graphs best represents the following function?

**Possible Answers:**

None of these

**Correct answer:**

The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve.

### Example Question #2 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

What is the equation of a parabola with vertex and -intercept ?

**Possible Answers:**

**Correct answer:**

From the vertex, we know that the equation of the parabola will take the form for some .

To calculate that , we plug in the values from the other point we are given, , and solve for :

Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term:

Distribute the fraction through the parentheses:

Combine like terms:

### Example Question #3 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Which graph depicts a function?

### Example Question #3 : How To Graph A Function

Which equation best represents the following graph?

**Possible Answers:**

None of these

**Correct answer:**

We have the following answer choices.

The first equation is a cubic function, which produces a function similar to the graph. The second equation is quadratic and thus, a parabola. The graph does not look like a prabola, so the 2nd equation will be incorrect. The third equation describes a line, but the graph is not linear; the third equation is incorrect. The fourth equation is incorrect because it is an exponential, and the graph is not an exponential. So that leaves the first equation as the best possible choice.

### Example Question #6 : How To Graph A Quadratic Function

**Possible Answers:**

None of the above

**Correct answer:**

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .

### Example Question #3 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

**Possible Answers:**

**Correct answer:**

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in form, we can tell straight away that this does not define a linear function because the value is to the second power.

Again, though this equation is not written in form, we can tell straight away that this does not define a linear function because the value is to the second power.

For this equation, we can solve for to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract from both sides:

Next, we can divide each side by

This equation is in slope-intercept form; thus, is the correct answer.

### Example Question #4 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

**Possible Answers:**

**Correct answer:**

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in form, we can tell straight away that this does not define a linear function because the value is to the second power.

Again, though this equation is not written in form, we can tell straight away that this does not define a linear function because the value is to the second power.

This equation is in slope-intercept form; thus, is the correct answer.

### Example Question #5 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

**Possible Answers:**

**Correct answer:**

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in form, we can tell straight away that this does not define a linear function because the value is to the second power.

Again, though this equation is not written in form, we can tell straight away that this does not define a linear function because the value is to the second power.

For this equation, we can solve for to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract from both sides:

Next, we can divide each side by

This equation is in slope-intercept form; thus, is the correct answer.

### Example Question #5 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

**Possible Answers:**

**Correct answer:**

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

For this equation, we can solve for to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

We can add to both sides:

This equation is in slope-intercept form; thus, is the correct answer.

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### All Common Core: 8th Grade Math Resources

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