Identify the Vertex
What is the vertex of
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.
What is the highest point the projectile reaches?
(2,10) which means in 2 seconds, the object reached 10 feet.
What is the equation for the axis of symmetry of f(x) = 3(x - 4)2 - 6?
x = 4
What is the domain of the parabola:
y = x2 − 4x + 5
Domain: x = All Real Numbers
Convert the following quadratic equation from vertex form to standard form.
y =(x + 2)2 + 2
y = x2 + 4x + 6
What is the vertex of
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
Identify the range of:
y = x2 − 4x + 2
Range: y>-2 or
y is the set of all real numbers greater than -2.
Convert the following quadratic equation from vertex form to standard form.
y =(x + 2)2
y = x2 + 4x + 4
What is the vertex of
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
What is the domain of the given quadratic function:
y = −2x2 −12x − 12
Domain: x = All Real Numbers
Convert the following quadratic equation from vertex form to standard form.
y = 2(x + 2)2
y = 2x2 + 8x + 8
What is the vertex of
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
What is the range of:
y = -2x2 +3
Range: y < 3 or
y is the set of all real numbers less than 3.
Convert the following quadratic equation from vertex form to standard form.
y = 3(x + 2)2 + 2
What is the vertex of
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
What is the domain and range of:
y = −8x2 − 80x − 199
Domain: x = All Real Numbers
Range: y > 1 or
y is the set of all real numbers less than 1.
Convert the following quadratic equation from vertex form to standard form.
y = -(x – 1)2 – 1
y = -x2 + 2x -2