Question

"a frog is sitting on a stump 12 feet above the ground. it hops off the stump and lands on the ground 6 feet away. during its​ leap, its height h is given by the equation h equals negative 0.5 x squared plus x plus 12 where x is the distance in feet from the base of the​ stump, and h is height in feet. how far was the frog from the base of the stump when it was 0.5 feet above the​ ground?"

Answer 1

Given equation: h = -0.5x² + x + 12

h = 0.5

-0.5x² + x + 12 = 0.5

-0.5x² + x + 11.5 = 0

Find the roots of quadratic equation.

x = ((-b )+- √(b² - 4ac))/2a

= ((-1 )+- √(1² - 4*(-0.5)*(11.5)))/2(1)

= -3.9, 5.9

The distance will not be negative.

Hence, the distance is 5.9.