Maria A. answered • 12/04/19

1. The vertex of a parabola occurs when x = -b/2a. In this case, b = 150, and a = -16. Therefore:

x = -(150) / 2* (-16) =-150/-32 = 4.685

By rounding this number to the nearest ones place, you get 4.7

2. The maximum height of the rocket occurs at the vertex. We know this because a is negative, and thus the parabola is facing downwards. To get the maximum height, plug x into the equation and solve for y:

y = -16(4.685)^2+150(4.685)+5 = 356.5624

By rounding this number to the nearest ones place, you get 356.6 feet

3. The easiest way to see if a quadratic equation is factorable is to look at the discriminant, which is b^2-4ac. The equation will only be factorable if the discriminant is a square number. In this case:

(150)^2 - 4 * (-16) * (5) = 22500 + 320 = 22820

22820 is not a square number, and therefore the equation is not factorable.

4. The rocket will hit the ground at the second y-intercept. Thus, we can set y=0 and solve for x.

0 = -16x^2 + 150 x + 5

By using the quadratic equation:

x = (-b+sqrt(b^2-4ac))/2a = (-150 +sqrt( (150)^2 - 4 * (-16) * (5)) /2*-16 = 0.0332156563

By rounding to the nearest tenths place, you get 0.03 seconds.