^{2}+x+24, we use 21.12 for h

^{2}+x+24

^{2}+x+2.88

^{2}-4ac)

^{2}-4(-0.5)(2.88))

a frog is sitting on a stump 24 ft above the ground. it hops off the stump and lands on the ground 8 ft away. during its leap, its height h is given by the equation h=-0.5x^2+x+24 where x is the distance from the base to the stump, and h is height in ft. how far was the frog from the base of the stump when it was 21.12 ft above the ground?

Simplify the answer. type an integer or a decimal. round to nearest tenth if needed.

Tutors, sign in to answer this question.

Pete R. | Experienced Math TutorExperienced Math Tutor

21.12 represents the height (h) of the frog

Using the formula h=-0.5x^{2}+x+24, we use 21.12 for h

21.12 = -0.5x^{2}+x+24

0=-0.5x^{2}+x+2.88

I'd suggest the quadratic equation

x= -b± √(b^{2}-4ac)

2a

a=-0.5

b=1

c=2.88

x= -1 ± √(1^{2}-4(-0.5)(2.88))

2(-0.5)

Simplifying

x= -1 ± √(6.76) = 1 ± 2.6

-1

So, the solution is x=3.6 OR -1.6 BUT!!:

since x represents the distance from the base to the stump, the distance is NOT negative.

So, our answer is:

x = 3.6 ft

It is as follows: h will be 21.12 and the equation that gives the height at any moment is h = -0.5X^2 + X +24

Checking this equation for x = 0 and x = 8 the equation is true.

so plugging the 21.12 into the equation we have: 21.12 = -0.5 X^2 + X +24, the equation is now:

-0.5 X^2 + X + 2.88 = 0

solving this quadratic equation, we obtain:

X=-b +-((b^2 - 4*a*c)^0.5)/2*a Being b = 1; c = 2.88; a= -0.5

X1=3.6

X2= - 1.6

the answer is 3.6 feet from the base because the negative value in not logic.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.