a flea's jump can be modeled by the function y = -0.073x(x-33) where x is the horizontal distance (in cm) and y is the corresponding height (in cm). How far did the flea jump? What was the flea's maximum height?

Question

a flea's jump can be modeled by the function y = -0.073x(x-33) where x is the horizontal distance (in cm) and y is the corresponding height (in cm).  How far did the flea jump? What was the flea's maximum height?

anonymous · Answer

are they askiing for the distance from when the flea would start from the ground or the distance from the height to the ground

anonymous · Answer

both

campbell_st · Answer

for the horizontal distance you need to find the values of x where the height is zero... 

this will give the horizontal distance. So solve

$$0 = -0.073x(x - 33)$$



the equation for the path is a quadratic so the flea jumps in a parabolic arc. 

to find the vertical height you can either distribute and get the equation 

$$y = -0.073x^2 + 2.409 x$$

find the line of symmetry   $$x = \frac{-b}{2a}$$  a = -0.073  b = 2.409

the max height can be found by substituting this value into the original equation. 

or

you can say the vertical height is a max at half the horizontal distance and substitute that value into the original equation. 

or

find the 1st derivative ( if you know calculus) and solve for x.... then substitute that value into the original equation.