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.
What is the equation for the axis of symmetry of f(x) = 3(x - 4)2 - 6?
x = 4
Use the information provided to write the vertex form equation of the parabola.
y = x2 − 4x + 5
y = (x−2)2 +1
Convert the following quadratic equation from vertex form to standard form.
y =(x + 2)2 + 2
y = x2 + 4x + 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
What is the equation for the axis of symmetry of f(x) = 5(x - 6)2 - 7?
x = 6
Use the information provided to write the vertex form equation of the parabola.
y = x2 − 4x + 2
y = (x−2)2 −2
Convert the following quadratic equation from vertex form to standard form.
y =(x + 2)2
y = x2 + 4x + 4
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
What is the axis of symmetry of f(x) = 9(x+8)2 + 47?
x = -8
Use the information provided to write the vertex form equation of the parabola.
y = −2x2 −12x − 12
y = −2(x+3)2 +6
Convert the following quadratic equation from vertex form to standard form.
y = 2(x + 2)2
y = 2x2 + 8x + 8
f(x) = 5x2
(0, 0)
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
What is the axis of symmetry of y = 5x2?
x = 0
Use the information provided to write the vertex form equation of the parabola.
y = 2x2 +3
y = 2x2 +3
Convert the following quadratic equation from vertex form to standard form.
y = 3(x + 2)2 + 2
f(x) = 2(x-9)2 - 47
(9, -47)
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.
What is the axis of symmetry of y = 4x2 + 16x + 3?
x = -2
Use the information provided to write the vertex form equation of the parabola.
y = −8x2 − 80x − 199
y = −8(x+5)2 +1
Convert the following quadratic equation from vertex form to standard form.
y = -(x – 1)2 – 1
y = -x2 + 2x -2