### All Algebra 1 Resources

## Example Questions

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

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 #1 : Graphing Polynomial Functions

**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 #2 : Graphing Parabolas

Which of the following graphs matches the function ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

The graph has no -intercepts.

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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:

### Example Question #4 : How To Graph An Absolute Value Function

**Possible Answers:**

**Correct answer:**

### Example Question #5 : How To Graph An Absolute Value Function

**Possible Answers:**

**Correct answer:**

### Example Question #6 : How To Graph An Absolute Value Function

**Possible Answers:**

**Correct answer:**

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

A function is given by . Find .

**Possible Answers:**

**Correct answer:**

Plugging in 2 wherever is present in the formula yields an answer of 14.