Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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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:

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

Possible Answers:

 

 

 

None of the above

 

Correct answer:

 

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 ?

Possible Answers:

Graph2

Graph1

Graph

Graph3

Graph4

Correct answer:

Graph

Explanation:

Start by visualizing the graph associated with the function :

Graph5

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:

Graph6

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  :

Graph

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

Absolute_value

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

Possible Answers:

Correct answer:

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 

Possible Answers:

The graph has no -intercepts.

Correct answer:

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

Absolute_value

 

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

Possible Answers:

Correct answer:

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:

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

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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

Possible Answers:

Correct answer:

Explanation:

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

A function is given by .  Find .

Possible Answers:

Correct answer:

Explanation:

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

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