write the equation

Question

write an equation for a parabola with x-intercepts (-4,0) and (2,0) which passes through the point (1,-10)

Answer 1

(-4,0), (2,0) have a midpoint (-1,0) x=-1 is the axis of symmetry

f(x)=y = a(x-2)(x+4)= a(x^2+2x-8)

plug in the point (1,-10) to solve for "a" the leading coefficient

-10 = a(-1)(5)

a = -10/-5 = 2

f(x)= 2(x-2)(x+4)

y=2(x-2)(x+4) in x intercept form, x intercepts 2 and -4

y=2x^2 +4x -16 where y intercept-1

y=2(x^2 +2x +1) -16-2

y = 2(x+1)^2 -18 in vertex form vertex = (-1,-18)

y(-1) = 2(-3)(3) = -18

the vertex = (-1,-18)

It's an upward opening parabola with y intercept =(0,-16), x intercepts (2,0),(-4,0)