Key Features of Quadratic Graphs

Activity 5.1: Characteristics of Quadratic Functions

​EQ: How can you determine key attributes of a quadratic function from an graph or equation?

Multiple Choice

What is a parabola?

• The straight graph of a quadratic function

• The circular graph of a quadratic function

• The V-shaped graph of a quadratic function

• The U-shaped graph of a quadratic function

Multiple Choice

Which letter determines if a parabola opens up or down?

• a

• h

• k

• c

• b

Multiple Choice

Tell whether the graph the quadratic function opens upward or downward.

$$y=-5x^2$$  

• Upward

• Downward

Multiple Choice

Tell whether the graph the quadratic function opens upward or downward.

$$y=5x^2+10$$  

• Upward

• Downward

Multiple Choice

What is the green dot on the parabola called?

• x-Intercept

• Vertex

• y-Intercept

• Zeros

Multiple Choice

A line about which a figure is symmetric is the:

• Solution Set
• Intercept Formula
• Quadratic Function
• Axis of Symmetry

Multiple Choice

Does this parabola have a maximum or minimum value?

• maximum

• mininmum

Multiple Choice

Does this graph have a maximum or minimum?

• Minimum
• Maximum

Multiple Choice

What is the vertex?

• (2, 4)
• (3, -1)
• (0, 8)
• (4, 2)

Multiple Choice

What is the vertex of the graph?

• (1,0)

• $$\infty$$  

• (0,0)

• None

Multiple Choice

What is the equation for axis of symmetry?

• y=3

• x=3

• x=5

• x=1

Multiple Choice

What is the axis of symmetry for this graph?

• y=2
• x=2
• x=0
• y=0

Multiple Choice

What is the axis of symmetry of the quadratic function?

• (- 4, 0)

• (0 , 0)

• x = -2

• y = -2

Multiple Choice

What are the coordinates of the y-intercept?

• (-3, 0)
• (0, -3)
• (2, 1)
• y=-3

Multiple Choice

What is the y-intercept of the quadratic function?

• (- 4, 0)

• (0 , 0)

• x = -2

• Can't be Determined

Multiple Choice

What is the RANGE of the function?

• $$\infty$$   

• $$y\ \ge\ 5$$  

• $$y\ \le\ 5$$  

Multiple Choice

What is the DOMAIN of this Function

• $$y\ge-1$$  

• $$y\le-1$$  

• $$\infty$$  

Multiple Choice

What is the RANGE of this function?

• $$y\le-2$$  

• $$y\ge-2$$  

• $$\infty$$  

Multiple Choice

What is the DOMAIN of this quadratic function?

• $$\infty$$  

• x ≥ 4
• x < 2
• x ≤ 4

Multiple Choice

Define Zeros in relation to Quadratic Functions

• Where the parabola touches or intersects the x- axis, also called the x-intercept

• A line that divides the graph into two equal parts. i.e. cuts the graph in half

• The highest or lowest point on the graph

• Where the parabola touches or intersects the y-axis

Multiple Choice

How many Zeros(s) does this graph have?

• One

• Two

• No solutions

Multiple Choice

What are the Zero(s) to the Graph?

• None

• (0,0)

• (1,0)

• $$\infty$$  

Multiple Choice

What are the Solution(s) to this Quadratic Graph?

• None

• One: (0,0)

• Two: (0,0) and (4,0)

Multiple Choice

What are the Zero(s) of the Graph?

• None

• (3,0)

• (2,0) (4,0)

• (0,8)

Multiple Choice

What is the significance of the ordered pair (2, -4) to the graph?

• It is the vertex

• It is an x-intercept

• It is the y-intercept

• It is the axis of symmetry

Multiple Choice

What is the significance of the point (0, 5)?

• x-intercept

• Axis of Symmetry

• Vertex

• y-intercept

Multiple Choice

What is the significance of the ordered pair (0, -2) to the graph?

• It is the vertex

• It is an x-intercept

• It is the y-intercept

• It is the axis of symmetry

Multiple Choice

Which statement about the graph is FALSE?

• The vertex is (-3, 18)

• The vertex is a maximum

• The y-intercept is y = 0

• The axis of symmetry is y = -3

Fill in the Blanks

For the equation $h\left(x\right)=x^2-2x+6$  evaluate  $h\left(0\right)$ . Write only the number as your answer.

Fill in the Blanks

For the equation $f\left(x\right)=-2x^2+8x$  evaluate  $f\left(-1\right)$ . Write only the number as your answer.

Fill in the Blanks

For the equation $g\left(x\right)=x^2-9$  evaluate  $g\left(5\right)$ . Write only the number as your answer.