Need help please Algebra! Given a function with a maximum value of y=8 and zeros x=2 and x=-6,

Question

Given a function with a maximum value of y=8 and zeros x=2 and x=-6, determine the equation of the function in all three forms (standard, vertex, and factored)

Answer 1

take the average of the x intercepts. That gives the axis of symmetry

x=-2, if y = the maximum = 6

then the vertex of the downward opening parabola = (-2,6)

That gives 3 points on the parabola

y-6 = a(x+2)^2 plug in either of the 3 points to solve for a, such as the vertex

6-6 =a(0)

try another point, an x intercept

0-6 = a(-6+2)^2 = 16a

a = -6/16 = -3/8

the parabola quadratic equation is

y-6 = (-3/8)(x+2)^2

or expand and eliminate fractions, combine like terms

3x^2 + 12x +8y = 36