Factored Form of Quadratic Functions

Factored Form of Quadratic Functions

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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

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.

Graphing

Graph y = (x-2)(x+4)

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

Graphing

Graph y = -(x+3)(x-1) careful with the negative.

Graphing

Sketch the graph the function

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