Quadratic Functions Unit 9

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Axis of Symmetry

A line that divides a figure in half so that each half is the mirror image of the other

x=3

A parabola has a vertex at ( 3,1). What is its axis of symmetry?

y=-2(x+3)²+6

Convert the following standard form equation to vertex form: y=-2x²-12x-12

y=-(x+3)²-1

Convert the following standard form equation to vertex form: y=-x²-6x-10

y=(x-6)²

Convert the following standard form equation to vertex form: y=x²-12x+36

y=(x-1)²-2

Convert the following standard form equation to vertex form: y=x²-2x-1

y=(x-2)²-2

Convert the following standard form equation to vertex form: y=x²-4x+2

minimum, up

Does the following graph have a maximum or minimum? Does it open up or down?: y=900(x-9)²+1

max; y = -3

Does the graph have a minimum or maximum and at what value?

min; y = -4

Does the graph have a minimum or maximum and at what value?

(-7, -10)

Find the vertex. y=-x²-14x-59

(-2, 8)

Find the vertex. y=2x²+8x+16

(7, -49)

Find the vertex. y=x²-14x

(-2, 3)

Find the vertex: -(x+2)^2 +3

(1, -1)

Find the vertex: y = (x-1)^2 -1

$7000

Given the graph shown, what is the maximum profit the tutoring business can make.

a= 1, b = 4, and c = -10

Given y = x^2 + 4x - 10, what are a, b, and c

x = 3

Identify the axis of symmetry:

(0, 7)

Identify the y-intercept:

none

Identify the zeroes (x-intercepts):

The most basic function of a family of functions, or the original function before a transformation is applied

Parent Function

parabola

The graph of a quadratic function forms a

100 ft

The height of a ball t seconds after it's thrown into the air from the top of a building can be modeled by h(t) = -16t^2 + 48t + 64, where h(t) is height in feet. How high does the ball rise before starting to drop downward?

64 ft

The height of a ball t seconds after it's thrown into the air from the top of a building can be modeled by h(t) = -16t^2 + 48t + 64, where h(t) is height in feet. How high is the building?

vertex

The highest or lowest point on a parabola is called the

maximum

The y-coordinate of the vertex of a parabola that opens DOWNWARD is called the

Minimum

The y-coordinate of the vertex of a parabola that opens UPWARD is the

x-intercept of the graph

The zero of a function is the...

Vertex

What form is the quadratic?

All real numbers

What is the domain of the graph?

all real numbers

What is the domain of this function?

y > -4

What is the range of the graph?

y < -4

What is the range of this function?

(-2, -5)

What is the vertex of f(x) = -½(x + 2)² - 5

(-5, 6)

What is the vertex of y= 9(x+5)² + 6

(0,8)

What is the y-intercept of the following equation: y=(x+3)²-1

Exponential

What type of function is this?

Linear

What type of function is this?

Quadratic

What type of function is this?

y = -x^2 - 3

Which equation can represent the parabola in the diagram?

y = -x^2 + 4

Which is an equation of the parabola graphed in the accompanying diagram?

y-intercept

Which of the following does not belong? root solution zero y-intercept

f(x)=(x-1)²

Write the function rule.

f(x)=2(x-4)²

Write the function rule.


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