Algebra 1 : How to graph a quadratic function

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #5 : Graphing Parabolas

Which is the graph of ?

Possible Answers:

Graph1

Graph3

Graph2

Graph4

Graph

Correct answer:

Graph

Explanation:

Think of the graph of :

Graph5

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:

Graph6

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:

Graph

Example Question #1 : How To Graph A Quadratic Function

What is the minimum possible value of the expression below?

Possible Answers:

The expression has no minimum value.

Correct answer:

Explanation:

We can determine the lowest possible value of the expression by finding the -coordinate of the vertex of the parabola graphed from the equation . This is done by rewriting the equation in vertex form.

The vertex of the parabola  is the point .

The parabola is concave upward (its quadratic coefficient is positive), so  represents the minimum value of . This is our answer.

Example Question #1 : How To Graph A Quadratic Function

What is the vertex of the function ? Is it a maximum or minimum?

Possible Answers:

; minimum

; maximum

; maximum

; minimum

Correct answer:

; minimum

Explanation:

The equation of a parabola can be written in vertex form: .

The point  in this format is the vertex. If  is a postive number the vertex is a minimum, and if  is a negative number the vertex is a maximum.

In this example, . The positive value means the vertex is a minimum.

Example Question #2 : How To Graph A Quadratic Function

Which of the graphs best represents the following function?

Possible Answers:

Graph_exponential_

Graph_parabola_

None of these

Graph_cube_

Graph_line_

Correct answer:

Graph_parabola_

Explanation:

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.

Graph_parabola_

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

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 .

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