This is the question, please dont just weite the answer, explain how you got it please:
Brett is jumping on a trampoline in his backyard. Each jump takes about 2 seconds from beginning to end. He passes his bedroom window, which is 4 m hugh, 0.4 seconds into each jump. By modelling Brett's height with a quadratic relation, determine his maximum hight.
Brett is jumping on a trampoline in his backyard. Each jump takes about 2 seconds from beginning to end. He passes his bedroom window, which is 4 m hugh, 0.4 seconds into each jump. By modelling Brett's height with a quadratic relation, determine his maximum hight.
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"Each jump takes about 2 seconds from beginning to end."
"About" doesn't do you much good. Assume that each jump lasts exactly 2 seconds.
His height is 0 at t = 0 seconds and t = 2 seconds.
"He passes 4 m height after 0.4 seconds"
Now you know three points: (0.4, 4), (2, 0), (0, 0), where the x-coordinate is the time in seconds, and the y-coordinate is the height.
A quadratic equation has the form ax² + bx + c = y. Plug in the three points to get a system of three equations:
Ⅰ. 0.16a+0.4b+c = 4
Ⅱ. 4a+2b+c = 0
Ⅲ. 0a + 0b + c = 0
Solve the system to get
a = -6.25
b = 12.5
c = 0
The equation becomes
-6.25x² + 12.5x = y
This is a down-opening parabola. In vertex form the equation becomes
y = -6.25(x - 1)² + 6.25
The vertex is (1, 6.25).
His maximum height is 6.25 meters.
"About" doesn't do you much good. Assume that each jump lasts exactly 2 seconds.
His height is 0 at t = 0 seconds and t = 2 seconds.
"He passes 4 m height after 0.4 seconds"
Now you know three points: (0.4, 4), (2, 0), (0, 0), where the x-coordinate is the time in seconds, and the y-coordinate is the height.
A quadratic equation has the form ax² + bx + c = y. Plug in the three points to get a system of three equations:
Ⅰ. 0.16a+0.4b+c = 4
Ⅱ. 4a+2b+c = 0
Ⅲ. 0a + 0b + c = 0
Solve the system to get
a = -6.25
b = 12.5
c = 0
The equation becomes
-6.25x² + 12.5x = y
This is a down-opening parabola. In vertex form the equation becomes
y = -6.25(x - 1)² + 6.25
The vertex is (1, 6.25).
His maximum height is 6.25 meters.
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She got 0.16a + 0.4b + c = 4 by plugging in the first point into ax² + bx + c = y. You can solve for a in terms of b by using the second equation. Then plug into the first equation to solve for b. The third equation tells you c=0.
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