Denise G. answered • 12/11/19
Algebra, College Algebra, Prealgebra, Precalculus, GED, ASVAB Tutor
The ball will reach its max height at the vertex. To find the x coordinate of the vertex, you can use the equation:
x=-b/(2a) = -120/(2*(-20)) = 3 It will reach its max height at 3 seconds.
To find the max height, plug in x=3 into the original equation.
(-20)(32)+(120)(3)-70 = 110 ft is the max height
To find when it hits the ground, we need to plug in y=0 and solve
0=-20x2+120x-70 We can simplify this by dividing everything by -10
0=2x2-12x+7
Using the quadratic formula, the 2 solutions are x=0.65 and 5.43
Since it hits the max at 3 seconds, the first solution isn't valid.
The ball will hit the ground in 5.43 seconds
Arturo O.
Note that in this problem, the launch height is -70, which is below ground. The ball crosses the ground on the way up at x=0.65 and again on the way down at x = 5.35. I wonder if there was a typo in the uploaded problem statement, and that the constant in the parabola was supposed to be positive.12/12/19