Remediation 2.1 CFA Key Features

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

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

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

A positive quadratic will open....

• downward

• upward

Multiple Choice

A negative quadratic will open.....

• upward

• downward

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 Choice

What are the x-intercepts:

(x - 5)(x - 1) = 0

• (5,0) & (1,0)

• (5,0) & (-1,0)

• (-5,0) & (1,0)

• (-5,0) & (-1,0)

Multiple Choice

Which equation matches the x-intercepts x=5,-7 ?

• (x+5)(x-7)=0

• (x-5)(x+7)=0

• (x+5)(x+7)=0

• (x-5)(x-7)=0

Multiple Select

What are the green dots called? (Check as many as apply)

• roots

• vertex

• solutions

• x intercepts

Multiple Choice

Which quadratic equation models the parabola shown?

• y = (x-2)(x-5)

• y = (x+2)(x+5)

• y = -(x+2)(x+5)

• y = -(x-2)(x-5)

Multiple Choice

Sketch the graph the function

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

Multiple Choice

What is the domain of the function?

• $$\left(-\infty,\infty\right)$$

• (- $$\infty$$ , 0)

• To infinity and beyond

• (0, $$\infty$$ )

Multiple Choice

Determine this function's DOMAIN

• $$\left(-4,\infty\right)$$  

• All Real Numbers

• $$\left(-3,\infty\right)$$

• $$\left(-\infty,\ 4\right)_{ }$$  

Multiple Choice

What is the range of the function?

• All real numbers

• $$\left[4,\infty\right)$$

• $$\left(-\infty,4\right]$$

• $$\left(-\infty,1\right]$$

Multiple Choice

Determine this function's RANGE

• $$\left[-4,\infty\right)$$  

• $$\left(-\infty,\infty\right)$$

• $$\left[-3,\infty\right)$$  

• $$\left(-\infty,4\right]$$  

Multiple Choice

Identify the domain and range of the function.

• Domain: $$\left(-6,2\right)$$

  Range: $$\left(-3,5\right)$$

• Domain: $$\left(-\infty,\infty\right)$$

  Range: (-3,5)

• Domain: $$\left(-\infty,\infty\right)$$

  Range: $$\left[-3,\infty\right)$$

• Domain: $$\left(-\infty,\infty\right)$$

  Range: $$\left(-\infty,-3\right]$$

Multiple Choice

What is the domain and the range for the graph?

• Domain : (-2,2)
  Range : (0,4)

• Domain : (0,4)
  Range : (-2,2)

• Domain : $$\left(-\infty,\infty\right)$$
  Range : $$\left(-\infty,4\right]$$

• Domain : $$\left(-\infty,\infty\right)$$
  Range : $$\left[4,\infty\right)$$

Multiple Choice

Identify the y-intercept.

• (0, 1)

• (2, 1)

• (0, 3)

• (0, -3)

Multiple Choice

An axis of symmetry is...

• a vertical line

• a horizontal line

Multiple Choice

Name the Axis of Symmetry

• x = 1

• x = 0

Multiple Choice

Identify the vertex

• (2, 4)

• (3, -1)

• (4, 2)

• (0, 8)

Multiple Choice

Use the picture to find the vertex and axis of symmetry.

• Vertex: (8, 3); axis of symmetry: y=3

• Vertex: (8, 3); axis of symmetry: x=3

• Vertex: (3, 8); axis of symmetry: y=3

• Vertex: (3, 8); axis of symmetry: x=3

Multiple Choice

Does this Parabola have a maximum or a minimum?

• Maximum

• Minimum

• Neither

• Both

Multiple Choice

What is the minimum value?

• (-1,0)

• (1,-4)

• (0,-3)

• (3,0)

• (4,-1)