SOLUTION: A projectile follows a parabolic path whose height in meters, is given by the function f(x) = -x^2 +2x +2. Find the mazimum horizontal distance that the projectile may cover.

Question 980100: A projectile follows a parabolic path whose height in meters, is given by the function f(x) = -x^2 +2x +2.
Find the mazimum horizontal distance that the projectile may cover.
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To find the maximum horizontal distance, which represents x in our quadratic equation, we will need to use the quadratic formula to find x.

ax^2 + bx + c -----> -x^2 + 2x + 2

a = -1
b = 2
c = 2

quadratic formula:

----->

----->

----->

----->

----->

We will now disregard the - sign, because if we subtract the square root of 3 from 1, we will obtain a negative number. A projectile that has not yet moved will start at the point (0,0) on a graph (unless we are told the projectile starts off at a different height, in which case our y coordinate may be higher than 0), so our x coordinate cannot be a negative number. We only want to find the distance between the original x coordinate (0) and the x coordinate where the projectile lands.

----->

----->

Therefore, the maximum horizontal distance that the projectile may cover is approximately 2.732 meters.

On a graph, the parabola will look like the following (note that the x coordinate where the projectile lands is 2.732)

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