SOLUTION: A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a maximum height of 40 feet as it heads toward its target on a parabolic path. Find the equ

Question 1195810: A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a
maximum height of 40 feet as it heads toward its target on a parabolic path. Find the
equation that represents the height off the ground versus the distance travelled for this
rocket. State the equation in the form 𝑦 = 𝑎𝑥
2 + 𝑏𝑥 + 𝑐. [HINT: The path of the rocket is
an “upside down” parabola, with one of the x-intercepts at the origin and the other at
(20,0). We also know the y-value of the vertex. We can use this information to find “a”,
the coefficient of the x2
term. One way to find this is to plug the known values into the
factored form of the equation, ie. 𝑦 = 𝑎(𝑥 − 𝑟)(𝑥 − 𝑠)]
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a maximum height of 40 feet as it heads toward its target on a parabolic path. Find the equation that represents the height off the ground versus the distance travelled for this rocket
--------------
Put the apogee above the Origin.
3 points on the parabola are
A(-10,0), B(0,40) and C(10,0)
------------
y = ax^2 + bx + c is a parabola
---
Point A:
0 = a*(-10)^2 + b*-10 + c = 0
100a - 10b + c = 0
---
Point B:
a*0 + b*0 + c = 40 ---> c = 40
---
Point C:
a*(10)^2 + b*10 + c = 0
100a + 10b + c = 0
100a - 10b + c = 0 --- Point A
---------------------------------------- Subtract
20b = 0
b = 0
=================
100a - 10b + c = 0 --- Point A
100a + c = 0
100a + 40 = c
a = -0.4
=================
y = -0.4x^2 + 40 is the equation WITH the center at the Origin.

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