Solving Squares
Solve for x
x2 = 81
x = +-9
To complete the square, what number should go in for c?
x2 - 6x + c
c = 9
Write the following equation in vertex form
f(x) = x2 + 6x + 12
f(x) = (x + 3)2 + 3
Solve for x:
x2 − 2x − 3 = 0
x = 3, -1
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t)=-16t2 +16t + 480 where t is the time in seconds and h is the height in feet.
How high is the cliff Jason jumped off?
y-intercept: (0, 480)
The cliff is 480 feet high
Solve for c
3c2 = 108
c = +-6
To complete the square, what number should go in for c?
x2 - 12x + c
c = 36
Solve by completing the square. (Only counts if you show your
a2 + 14a − 51 = 0
(a + 7)2 - 100 = 0
a = 3, -17
Solve for x:
x2 + 14x − 15 = 0
x = 1, -15
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t)=-16t2 +16t + 480 where t is the time in seconds and h is the height in feet.
How high did Jason jump?
h(t) = -16(t - .5)2 + 484
Jason jumped 4 feet up off the cliff, for a maximum height of 484 feet.
Solve for m
5m2 + 10 = 135
m = +-5
To complete the square, what number should go in for c?
x2 + 8x + c
c = 16
Solve by completing the square. (Only counts if you show your work!)
5k2 + 20k − 60 = 0
5(k + 2)2 - 80 = 0
k = -6, 2
Solve for x:
x2 − 10x + 26 = 8
x = 5 +- sqrt(7)
DAILY DOUBLE!!!
A model rocket is launched from the roof of a building. Its flight path is modeled by h=-5t2+30t+10 where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds. What is the rocket's maximum height, and when does it reach that height?
h = -5(t - 3) + 55
(3, 55)
The rocket reaches 55 meters high at 3 seconds.
Solve for q
.5q2 - 4 = 20.5
q = +- 7
To complete the square, what number should go in for c?
x2 - 3x + c
c = 2.25
Solve by completing the square. (Only counts if you show your work!)
2c2 = −6 + 8c
2c2 - 8c + 6 = 0
2(c - 2)2 - 2 = 0
c = 3, 1
Solve for x:
x2 = 18x + 40
x = -2, 20
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t)=-16t2 +16t + 480 where t is the time in seconds and h is the height in feet.
At what point does Jason hit the water?
Jason hits the water at 6 seconds
Solve for x
3x2 - 4 = 2x2 + 9
x = +- sqrt5
To complete the square, what number should go in for c?
x2 + 5.5x + c
c = 7.5625
Solve by completing the square. (Only counts if you show your work!)
k2 − 12k + 23 = 0
(k - 6)2 - 13 = 0
k = 6 +-sqrt(13)
Solve for x:
8x2 + 16x = 42
x = 3/2, -7/2
The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle.
x(x+6) = 91
x = 7, -13(not valid answer)
Solve for j
j2 - 5 = -10
j = sqrt(5)i or NO SOLUTION
To complete the square, what number should go in for c?
3x2 - 6x + c
c = 1
Solve by completing the square. (Only counts if you show your work!)
3x2 - 6x = 12
3(x - 1)2 - 15 = 0
x = 1 +- sqrt(5)
Solve for x:
x2 + 81 = 19
x = +-10i
The hypotenuse of a right triangle is 6 more than the shorter leg. The longer leg is three more than the shorter leg. Find the length of the shorter leg.
x2 + (x + 3)2 = (x + 6)2
x = 9, -3(not a valid answer)