Quadratic Functions Unit 9
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.