Identify the Vertex
f(x) = x2
(0, 0)
The height of a projectile is modeled by the equation f(x) = -8(x-2)2 +10 where f(x) is the height in feet and x is the seconds.
After how many seconds is the projectile at its highest point?
What is the highest point the projectile reaches?
What is 2 seconds and 10 feet.
The equation of the parabola that has a vertex at (0,0) and goes through the point (1,1)
What is y = x2?
Use the information provided to write the vertex form equation of the parabola.
y = x2 − 4x + 5
y = (x−2)2 +1
The transformations of y = x2 + 6
What is up 6?
f(x) = (x + 2)2 + 4
(-2, 4)
The height of a ball, h meters, in t seconds is given by the function h = -5(t-3)2 + 46.5.
That is the maximum height of the ball?
46.5 meters
The equation of a parabola that has a vertex at (1, 2) and goes through the point (0, 3)
What is y = (x-1)2 + 2?
Use the information provided to write the vertex form equation of the parabola.
y = x2 − 4x + 2
y = (x−2)2 −2
The transformations of y = (x - 4)2 - 6
What is right 4 and down 6?
f(x) = (x-7)2
(7, 0)
The cost in C dollars of operating a machine per day is given by the function C= 2(x - 5)2 + 25.
What is the minimum cost to operate the machine?
$25
The equation of a parabola that has a vertex at (-3, 5) and goes through the point (-6, -4)
What is y = - (x +3)2 + 5?
Convert to standard form: y = (x - 3)2 + 5
y = x2 - 6x + 14
The transformations of y = -(x + 5)2 + 7
What is reflect over x-axis, left 5, and up 7?
f(x) = 2(x-9)2 - 47
(9, -47)
A quarterback passed the ball to a receiver 40 meters downfield. The path of the ball can be described by the equation h= (x - 2)^2 + 24 where x is seconds and h is meters.
When does the ball reach its maximum height?
2 seconds
The equation of this parabola crosses the x axis at -2 and 4 and goes through the point (0, -8).
What is y = (x +2)(x - 4)?
Convert to standard form: y = 3(x - 5)2 - 8
y = 3x2 -30x + 67
Given the transformations of the quadratic (x2), create the equation: right 3, up 2.
What is y = (x - 3)2 + 2
y = −2x2 −12x − 12
(-3, 6)
A missile is launched and the function f(x)= -2(x-18)^2 - 648 represents its path where f(x) is the height of the missile. A plane is flying at a height of 650 feet.
Is the plane in danger? Why?
No, because the missile only reaches 648 feet so it will not make contact with the plane.
The equation of this parabola crosses the x axis at -2 and 4 and has a vertex at (-1,9).
What is y = - (x+2)(x-4)?
Use the information provided to write the vertex form equation of the parabola.
y = −2x2 −12x − 12
y = −2(x+3)2 +6
Given the transformations of the quadratic (x2), create the equation: left 4, down 5, reflect down, stretch by 2.
y = -2(x +4)2 - 5