Quadratic Formula
Solve the following equation using the quadratic formula:
x2 - 14x + 45 = 0
What is x = 9,and x = 5
The equation of a parabola in vertex form with vertex (1, 4) and a-value of 2
What is y=2(x-1)2+4
A football throw can be measured by y=-x2-1x+12 where x represents seconds after it's thrown, and y represents the height of the football. How long does it take the football to reach the ground?
What is x=3 s
The equation h=-16t2+198t+25 represents the height of a diver jumping off a cliff after t seconds. What is the height of the diver after 5 seconds?
615 ft.
The function h=-16t2+40t+3 gives the height, in feet, of a tennis ball t seconds after someone hits the ball.
How high off the ground is the ball 2 seconds into its flight?
19 feet
Solve the following equation using the quadratic formula:
4x2 + 8x - 77 = 0
What is x = -5.5 and x = 3.5
The equation of a parabola in factored form with x-intercepts (3,0) and (-6,0), and an a-value of -0.5
What is y=-0.5(x-3)(x+6)
A bungee jumper decides to try a jump off of a new bridge. His jump can be measured by y=15x2-60x+72, where x represents time in seconds, and y represents his height in feet. When will the bungee jumper reach the lowest point in his journey?
What is x = 2s
A ball being thrown in the air can be modeled by the equation h=-4.9t2+14t+49. where h represents height in feet and t represents time in seconds. How long does it take for the ball to reach its maximum height?
1.43 sec
A rock is thrown directly up from a treehouse. The height of the rock t seconds after it is thrown is modeled by the equation h=-16t2+48t+20 where h is the height of the rock, in feet.
What is the height of the treehouse it was thrown from?
20 feet
Solve the following equation using the quadratic formula:
k2 - 10k + 35 = 7k - 35
What is k = 7 and k = 10
The equation in vertex form that satisfies the following key features:
y-int:(0,13) vertex:(3,4)
What is y=(x-3)2 +4
An object is launched directly upward from a platform 80 feet high, following the path h=-16t2+64t+80. What will be the object's maximum height? When will it attain this height?
What is when t = 2s, the maximum height is 144 feet.
The equation -15t2+60t+3 represents the height of a water balloon at t seconds. How long will it take for the water balloon to hit the ground?
3.95s
A video goes viral on social media, the number of views per day can be modeled with the equation y=-1.875x2+22.5x where x is the number of days after the video is posted and y is the number of views per day in thousands.
On what day do the most people watch the video?
Day 6
Solve the following equation using the quadratic formula.
6n2 + 4n - 20 = -n2
What is n = 10/7 and n = -2
An equation in factored form of a parabola with x-intercepts at (-4,0) and (0,0), and a vertex at (-2,8)
What is y=-2x(x+4)
The equation for a rocket's height h at time t seconds after launch is h=–4.9t2+19.6t+58.8, where h is in meters. When does the object strike the ground?
What is t = 6s
The equation P=-3x2+12x+2 represents the amount of P profit for the x cost of an item. What is the maximum profit for the sale if the item?
$14
Assume the equation S=-3x2+30x-3 models the sales of a recently released video game, where x is the number of weeks after release, and S is the number of weekly sales in millions.
According to this model, what are the peak weekly sales for the game?
$72 million
Solve the following equation by quadratic formula.
10x2 - 12x + 11 = -x2 + 2x - 7
What is "no real roots"
Given the following key features, write the corresponding equation in all 3 forms: (standard, factored, and vertex)
x-ints: (-7,0) & (1,0)
y-int:(0,7) vertex:(-3,16)
Standard: y=-x2 -6x + 7
Factored: y=-(x+7)(x-1)
Vertex: y=-(x+3)2 + 16
Angelina tosses a coin off a 112 foot high bridge into the stream below. The coin reaches a maximum height of 256ft, 3s after she tosses it. Write an equation in vertex form to model the path of the coin.
What is h=-16(t-3)2+256
h=-16t2+64t+80 represents the height of a rocket at t time in seconds. How long does it take the rocket to reach 100ft on its accent?
0.34 s
h=-16t2+64t+80 represents the height of a rocket at t time in seconds. For how long is the rocket above 100ft?
Approximately 3.32s