Factored Form

Factored Form of Quadratic Functions

Learning Objectives

• Identifying the x-intercepts of a Quadratic Function in Factored Form

• Finding the Vertex of a Quadratic Function in Factored Form

• Graphing a Quadratic Function in Factored Form

Factored Form of a Quadratic Function

The factored form of a Quadratic Function tells us the x-intercepts

x-intercepts are where the line crosses the x-axis

Multiple Choice

What are the x-intercepts of

$$f\left(x\right)=\left(x+3\right)\left(x+8\right)$$  ?

• (3,0) and (8,0)

• (-3,0) and (-8, 0)

• (-3, 0) and (8,0)

• (3, 0) and (-8, 0)

Multiple Choice

What are the x-intercepts of

$$y=\left(x-6\right)\left(x+4\right)$$  ?

• (3, 0) and (-2, 0)

• (-6, 0) and (4, 0)

• (6, 0) and (-4, 0)

• (-6, 0) and (-4, 0)

Multiple Select

What are the x-intercepts of

$$f\left(x\right)\ =\ \left(x-3\right)\left(x+8\right)$$  ?

• x = 3

• x = -8

• x = -3

• x = 8

Finding the Vertex

We know that factored form gives us the x-intercepts. How do you find the vertex?

Since Parabolas are symmetric, the x coordinate of the vertex will lie mid way between the two x-intercepts.

Plug in that x into the equation to find the y-coordinate.

Multiple Select

What is the mid point between x = 2 and x = -4?

• x = -1

• x = 0

• x = -2

Fill in the Blank

We know that the function

$$f\left(x\right)\ =\ \left(x-2\right)\left(x+4\right)$$  has x-intercepts at x = 2, and x = -4. The midway between x =2 and x = -4 is x = -1. If you plug in x = -1 in the equation, what should you get as the y value?

Finding the Vertex

Graphing a Quadratic in Factored Form

• Identify the two x-intercepts.

• Determine the x coordinate of the vertex; the midway between the two x-intercepts.

• Plug the x coordinate of the vertex into the equation to find the y coordinate

• use those 3 points to sketch the graph of the parabola.

has x-intercepts at (2,0) and (-4,0). We calculated the vertex to be (-1,9). Click on image to enlarge it.

Multiple Choice

Sketch the graph the function

$$f\left(x\right)\ =\ \left(x-3\right)\left(x+3\right)$$  

Multiple Choice

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

• (-5, 0) and (9, 0)

• (5,0) and (-9, 0)

• (5, 0) and (9, 0)

• (-3, 0) and (5, 0)and (-9, 0)

Multiple Choice

What are the x-intercepts of the parabola?

y = ¼(x + 2)(x - 6)

• (-2, 0) and (6, 0)

• (2, 0) and (-6, 0)

• (-2, 6)

• (¼, 0) and (-2, 0) and (6, 0)

Multiple Choice

State the direction of opening of the following: y = -(x+3)(x-2)

• Left

• Up

• Down

• Right

Multiple Choice

What are the x-intercepts of the quadratic?

• (2, 0) and (4, 0)

• (-2, 0) and (-5, 0)

• (2, 0) and (5, 0)

• (-2, 0) and (-4, 0)

Multiple Choice

What is the green dot on the parabola called?

• vertex

• minumum

• roots

• zeros

Multiple Choice

Identify and classify the vertex.

• (-6,5); minimum

• (-6,5); maximum

• (5,-6); minimum

• (5,-6); maximum