Characteristics of Quadratic Functions

Characteristics of Quadratic Functions

by: Ph-USA Guru

Multiple Choice

What is the standard form of a Quadratic function?

• ax²+bx+c

• ax²+bx-c

• ax²-bx+c

• ax²-bx-c

Multiple Choice

(0,0) on this graph is the...

• vertex and minimum
• vertex and maximum
• symmetry point
• range

Multiple Choice

The vertex of the parabola is the...

• maximum 
• minimum
• axis of symmetry
• line of symmetry

Multiple Choice

What's the vertex of the parabola?

• (-2,4)

• (-1,1)

• (0,0)

• (2,4)

Multiple Choice

Domain is the set of ___ values of a relation.

• X

• Y

Multiple Choice

Range is the set of ___ values of a relation.

• X

• Y

Open Ended

Type your favorite number if you are ready.

Axis of Symmetry (AOS)

• A VERTICAL line that divides the graph of a function into mirror images.

Multiple Choice

What is the axis of symmetry?

• the slope of the graph

• the dividing line for a parabola

• a way to spin my pencil

• the x-axis

Multiple Choice

Find the axis of symmetry for

f(x) = x²- 8x + 15.

• x = -4

• x = 4

• y = 4

• y = -4

Multiple Choice

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

• y = -2
• x = 3
• x = -3
• y = 2

Multiple Select

Can you identify the axis of symmetry (AOS) in the graph now?

• Yes

• NO

• I need more example.

VERTEX

• •The point on the parabola that lies on the axis of symmetry.

Multiple Choice

Given: y = 2(x - 5) + 6, the vertex is

• (2, -5)

• (-5, 6)

• (2, 6)

• (5, 6)

Multiple Choice

What is the vertex of the function y = (x - 3)² + 5

• (-3, 5)

• (3, -5)

• (-3, -5)

• (3, 5)

X-intercepts

• •The point(s) at which a parabola crosses the x-axis.

Multiple Choice

What are the x-intercepts?

• 0 and 2
• -4 and 0
• 2 and 3
• 0 and 4

Y-intercepts

• The point(s) at which a parabola crosses the y-axis.

Multiple Choice

What is the y-intercept of 
f(x)=2x² + 4x + 6

• (6 , 0)
• (-6 , 0)
• (0, -6)
• (0 , 6)

Zero of Quadratic Functions

• A value k whereas f(k)=0. (The X - values of the x-intercepts.)

Multiple Choice

Name the x-intercept(s)?

• (0, 0)
• (2, 4)
• (0, 0) and (0, 4)
• (0, 0) and (4, 0)

Multiple Choice

The x-intercepts of a quadratic equation are known as the _____.

• vertices

• squares

• zeros

• formulas

Multiple Choice

Which is a zero of the graph?

• 0

• -1

• 1.5

• -3

Multiple Choice

What is another name for the x-intercepts of a quadratic?

• y-intercept

• Zeros

• x-axis

• They don't have another name

Multiple Choice

Calculate the zeros of the quadratic.

• x = 2 and -3

• x = 0 and 9/4

• x = 0 and 4/9

• x = 1/2 and 1/3

Open Ended

Can I move to the next slide now?

Maximum and Minimum Values

• The highest y-value.

• The lowest y-value.

Multiple Choice

Which of the following functions has a minimum value of -4?

Multiple Choice

What is the minimum value of the quadratic function?

• -3

• -1

• All real numbers

• 1

Multiple Choice

What do we call the highest or lowest point of a quadratic?

• parabola

• vertex

• graph

• point

Multiple Choice

Does the equation have a max or min?

y = 2x² + 7x + 5

• max

• min

Multiple Choice

Does the equation have a max or min?

y = 2x² + 7x + 5

• max

• min

Multiple Choice

Does

y = -4x²

have a maximum or minimum value?

• maximum

• minimum

Multiple Choice

What is the arrow pointing at? How can you use this value to determine the minimum/maximum values?

• The arrow is pointing at the y-intercept. The y value of this point is equivalent to the maximum/minimum

• The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum

• The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

• The arrow is pointing at the vertex. The y value is equivalent to the minimum/maximum

Multiple Choice

Determine if the function graphed has a maximum or a minimum value and identify that value.

• maximum at -1

• minimum at -1

• maximum at 4

• minimum at 4

Poll

• If yes, please type your question in the chat box, un mute yourself, or email me.

Journal Writing:

• Is there a difference between the zeros of functions and the x-intercepts?