Standard Form
What is the axis of symmetry for the equation
y = -x2 - 4x ?
x = -2
Write in vertex form: Quadratic function has a vertical shift down 4, vertical reflection, vertical stretch by a factor of 2, and a horizontal shift left 3
y = -2 ( x + 3 )2 - 4
A shoe is dropped from a height of 60 feet. The height of the shoe can be modeled with the equation h(t) = -5t2 + 60 where h is height in feet and t is time in seconds. When does the shoe land on the ground?
3.5 seconds
Solve by factoring: 3x2 - 11x = -10
x=5/3 and x = 2
Find the axis of symmetry:
f(x) = -3x2 + 6x - 7
x = 1
What is the y intercept for the function
y = 3x2 - x -11?
(0, -11)
Rewrite f(x) = x2 - 4x +3 in vertex form.
y = ( x - 2 )2 - 1
A softball is thrown at 19.6 meters per second from a 58.8 meter tall platform. The height of the softball is given by the function s(t) = -16t2 +19.6r + 58.8 where t is time in seconds. If nobody catches the softball, when does it land?
6 seconds
Solve by factoring: x2 - 8 = -2x
x = -4 and x = 2
Find the vertex: f(x) = -4x2 - 32x + 67
(-4, 131)
Find the x-intercepts: f(x) = x2 - 8x + 15
(3, 0) and (5,0)
Rewrite f(x) = 2x2 -16x + 34 in vertex form.
f(x) = 2(x - 4)2 -2
A rock is thrown in the air from a window that is 3 meters tall with an initial velocity of 14 m/s. Write a function that models the height of the ball over time.
h(t) = -16t2 + 14t + 3
Solve by completing the square:
x2 - 24 = 8x
x = 4 +/- 2*sqrt(10)
Find the vertex of f(x) = -x2 -2x - 5
(-1, -4)
State the max/min for the following function:
f(x) = 2x2 - 4x + 1
Min = -1 when x = 1
Rewrite f(x) = -x2 - 6x -10 in vertex form.
y = - ( x +3 )2 - 1
An arrow's height can be modeled by the function h(t) = -16t2 + 48t + 16 where h is the height in feet and t is time in seconds. When does the arrow reach its maximum height? What is its max height?
Reaches max height of 52 feet after 1.5 seconds
Solve by completing the square:
11x2 + 20x = -25 + 10x2
x = -10 +/- 5 * sqrt (3)
Given f(x) = x2 +8x + 13, find the vertex, axis of symmetry, max/min, and y-intercept.
Vertex: (-4, -3)
Axis of Symmetry: x = -4
Min is -3 @ x = -4
y-int: (0, 13)
Which of the following is true with respect to the
functions f(x) = x2 -5x +10 and g(x) = -3x2 -3x +10 ?
A They have the same vertex
B They have the same range
C . They have the same y intercept
C
f(x) = - ( x + 2 )2 - 3 g(x) = - ( x-6 )2 - 1
Which function has the greater maximum value? By how much?
g(x) has a greater maximum value by 2
A ball is thrown from a 128-meter tower with an initial vertical velocity of 32 m/s. When does the ball land on the ground?
Lands after 4 seconds
Solve by completing the square:
x2 = -3x + 5
x = (-3 +/- sqrt(29)) / 2
Write the equation in vertex form and state all transformations that occur on the function:
f(x) = -2x2 + 12x - 14
f(x) = -2 (x - 3)2 + 4
Vertical reflection, vertical stretch by a factor of 2, horizontal shift right 3, vertical shift up 4