What is a quadratic function with a maximum at #(3, 125)# and roots at #-2# and #8#?

Question

1049 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-25T22:13:18

#y=-5x^2+30x+80#

The two roots are #-2# and #8#. This means that the function can be written as

#y=a(x+2)(x-8)#

where #a# is some constant.

Plug in #(x,y)rarr(3,125)# to find what #a# must be.

#125=a(3+2)(3-8)#

#125=a(5)(-5)#

#125=-25a#

#a=-5#

Thus, the equation of the parabola is #y=-5(x+2)(x-8)#, or #y=-5x^2+30x+80#.

graph{-5x^2+30x+80 [-5, 12, -20, 140]}