Axis of Symmtrey and Vertex
Convert Forms
x-intercepts
y-intercept and discriminant
applications
100
Find the equation for the axis of symmetry
y = -3x2 - 42x - 159
x = -7
100
y = 5(x - 3)2 + 8
y = 5x2 - 30x + 53
100
Find the x-intercepts
y = x2 - 19x + 90
(10, 0) (9, 0)
100
Find the y-intercept
y = 4x2 - 3x + 15
(0, 15)
100
A rocket is launched in the air. Its height in feet is given by h(t) = -16t2 + 40t where t represents the time in seconds after launch. How many seconds have gone by when the rocket is at its highest point?
1.25 seconds
200
Find the equation for the axis of symmetry
x = -3
200
Convert to standard form
y = -5(x + 1)2 + 7
y = -5x2 - 10x + 2
200
Find the x-intercepts
y = 3(x - 8)2 - 51
200
Find the y-intercept
y = 6(x - 3)2 - 20
(0, 34)
200
A tennis ball is dropped from a certain height. Its height in feet is given by h(t) = -16t2 + 1444 where t represents the time in seconds after launch. How long is the ball in the air?
9.5 seconds
300
Find the coordinates of the vertex
y = 4(x - 5)2 + 2
(5, 2)
300
Convert to vertex form
y = x2 + 2x + 8
y = (x + 1)2 + 7
300
Find the x-intercepts
y = 4x2 - 8x - 5
(5/2, 0) (-1/2, 0)
300
What is the discriminant of the quadratic equation?
y = -9x2 - x - 5
-179
300
Terry launches a toy rocket from a platform. The height of the rocket in feet is given h(t) = -16t2 + 24t + 16 where t represents the time in seconds after launch. What is the rocket's initial height?
16 feet
400
Find the coordinates for the vertex
y = x2 - 6x + 4
(3, -5)
400
Convert to vertex form
y = x2 - 5x - 2
y = (x - 2.5)2 - 8.25
400
Find the x-intercepts
y = 4x2 - 5x - 4
400
What is the discriminant of the quadratic equation?
y = -x2 - 2x + 5
24
400
Zoe kicks a football. Its height in feet is given by h(t) = -16t2 + 56t where t represents the time in seconds after kick. What is the football's greatest height?
49 feet
500
Find the coordinates of the vertex
y = -3x2 + 24x - 45
(4, 3)
500
Convert to vertex form
y = 3x2 - 48x + 195
y = 3(x - 8)2 + 3
500
Find the x-intercepts
500
What is the discriminant of the quadratic equation?
y = 5x2 + 90x + 405
0
500
Lillian kicks a football. Its height in feet is given by h(t) = -16t2 + 72t where t represents the time in seconds after kick. How many seconds have gone by when the football is at its highest point?
2.25 seconds