# Algebra 1 : Functions and Lines

## Example Questions

### Example Question #2 : How To Graph A Quadratic Function

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

Explanation:

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 #1 : Graphing Polynomial Functions

None of the above

Explanation:

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 #2 : Graphing Parabolas

Which of the following graphs matches the function ?

Explanation:

Start by visualizing the graph associated with the function :

Terms within the parentheses associated with the squared x-variable will shift the parabola horizontally, while terms outside of the parentheses will shift the parabola vertically. In the provided equation, 2 is located outside of the parentheses and is subtracted from the terms located within the parentheses; therefore, the parabola in the graph will shift down by 2 units. A simplified graph of  looks like this:

Remember that there is also a term within the parentheses. Within the parentheses, 1 is subtracted from the x-variable; thus, the parabola in the graph will shift to the right by 1 unit. As a result, the following graph matches the given function  :

### Example Question #1 : How To Graph An Absolute Value Function

Which of these would most likely be the equation corresponding to the above graph?

Explanation:

This is an absolute value graph. Its equation takes the form , in which  represent the number of units that the base graph  is translated right and up respectively.

Since the graph of  is translated two units right and one unit down,  and , so the equation would be:

or

### Example Question #1 : How To Graph An Absolute Value Function

Give the -intercept(s) of the graph of the function

The graph has no -intercepts.

Explanation:

To find the -intercept(s) of the graph, set  and solve for .

Rewrite this as the compound equation:

or

Solve each separately:

There are two -intercepts:

### Example Question #2 : How To Graph An Absolute Value Function

Which of these would most likely be the equation corresponding to the above graph?

Explanation:

This is an absolute value graph. Its equation takes the form , in which  represent the number of units that the base graph  is translated right and up respectively.

Since the graph of  is translated three units left and six units down,  and .

Plug these values into the general form of the equation:

Simplify:

Explanation:

Explanation:

Explanation:

### Example Question #1 : How To Find F(X)

A function is given by .  Find .