SD THURS Quadratic Graphs and Equations

Hotspot

Mark the solutions to the quadratic function.

Choose all answers that apply.

Labeling

Label the Quadratic Function.

Drag labels to their correct position on the image

axis of symmetry

vertex (minimum)

vertex (maximum)

POSITIVE zero

y-intercept

NEGATIVE root

Multiple Choice

What is the equation of the axis of symmetry for this parabola?

• x = 1

• y = 3

• x = 3

• y = −4

​Standard Form

​Factored Form

​Vertex Form

Forms of Quadratic Functions

​Notice, all three function create the same parabola.

Red=Factored= Reveals zeros. {-3, 5}

Blue=Standard= Reveals y-intercept (0, -15)

Green=Vertex= Reveals the vertex. (1, -16)

Match

Match the following quadratic functions forms to what they most quickly reveal.

• $$f\left(x\right)=2x^2-3x+5$$

• $$f\left(x\right)=2\left(x-4\right)\left(x+3\right)$$

• $$f\left(x\right)=2\left(x-5\right)^2+3$$

y-intercept (0,5)

x-intercepts at x=-3 and x=4

vertex

(5, 3)

• y-intercept (0,5)

• x-intercepts at x=-3 and x=4

• vertex

  (5, 3)

Multiple Choice

What is the vertex?
y = -2x² + 4x + 3

• (0, 3)
• (-1, 5)
• (1, 5)
• (1, -5)

Multiple Choice

WHICH GRAPH REPRESENTS THE QUADRATIC FUNCTION?

• A
• B
• C
• D

Multiple Choice

WHICH GRAPH REPRESENTS THE QUADRATIC FUNCTION?

• A
• B
• C
• D

Multiple Choice

Which quadratic function is graphed?

• $$y\ =\ -5x^2-20x+13$$

• $$y\ =\ 5x^2-20x+13$$

• $$y\ =\ x^2-4x+13$$

• $$y=5x^2+20x-13$$

Multiple Choice

Find the root(s) of this parabola?

• x = 4, y = 0

• x = 4

• x = 0, x = 4

• x = −4, y = 0

Match

Match the following quadratic expressions from their standard form to their factored form.

• $$x^2+10x+25$$

• $$x^2-16$$

• $$x^2+8x+16$$

• $$x^2-25$$

• $$x^2+8x+12$$

• $$\left(x+5\right)\left(x+5\right)$$

• $$\left(x+4\right)\left(x-4\right)$$

• $$\left(x+4\right)^2$$

• $$\left(x-5\right)\left(x+5\right)$$

• $$\left(x+2\right)\left(x+6\right)$$

Draw

Complete the input output table for the quadratic function $$y\ =\ -3x^2+6x-6$$ .

Multiple Choice

What is the domain of $$y=-3x^2+6x+4$$ ?

• All real numbers

• $$y\le7$$  

• $$x\le7$$  

• $$x\le4$$  

Multiple Choice

What are the domain and range of the graph?

• Domain: all real numbers

  Range: $$y\ge5$$  

• Domain: all real numbers

  Range: $$y\le5$$  

• Domain: $$1\le x\le6$$  

  Range: $$y\ge-5$$  

• Domain: $$1\le x\le6$$  

  Range: $$y\le5$$  

Multiple Choice

What is the range of $$p\left(x\right)=8x^2-16x+4$$ ?

• $$y\ge-4$$  

• $$y\le-4$$  

• $$y>-4$$  

• $$y<-4$$  

Draw

Label the axis of symmetry and the vertex of this quadratic formula.

Multiple Choice

Given f(x) = (x + 6)² - 2 , how did f(x) transform from the parent function?

• Horizontal shift left 6, vertical shift up 2

• Horizontal shift left 6, vertical shift down 2

• Horizontal shift right 6, vertical shift down 2

• Horizontal shift right 6, vertical shift up 2