how do you find the equation for a graph with x-intercepts of (2,0) and (-6,0) and a maximum point of (-2,4)

Question

how do you find the equation for a graph with x-intercepts  of (2,0) and (-6,0) and a maximum point of (-2,4)

amistre64 · Answer

thats a quadratic

amistre64 · Answer

the most basic approach is to solve for 3 equations with variables of a b and c; using your x and y values as your quadratic constants

amistre64 · Answer

or...or   factor in the roots

amistre64 · Answer

(x-2)(x+6)

amistre64 · Answer

C(x^2 +4x -12) is the family of quadratics with these roots

amistre64 · Answer

if we complete the square and plug in for the vertex we got it solved

amistre64 · Answer

x^2 +4x +4 = 12+4

(x+2)^2 = 16

amistre64 · Answer

(-1/4)(x+2)^2 +4 = y might be it

amistre64 · Answer

lets check it out :)

amistre64 · Answer

-1/4(x^2 +4x-12)

-x^2/4 -x +3

1/2(-1/4) = 1/(-2/4) = 1/(-1/2) = -2  x is good

amistre64 · Answer

-1/4(x^2 +4x -12)  |x=-2

(-1/4)(4 -8 -12) = -16/-4 = 4

YES

amistre64 · Answer

now that I taught mysef something, any questions lol

anonymous · Answer

no

amistre64 · Answer

:)  good, cause I dont know if I can remember how I did it ;)