Write an equation of a parabola intercept form.

Question

X intercept of 12 and -4 and passes through (16,50)

Answer 1

y=(5/8)(x-4)^2 -40 is the upward opening parabola with roots -4 & 12 going through (16,5)

axis of symmetry is x=4. 4 is the midpoint between the 2 roots, or their average (12+4)/2 = 8 added to -4=4

or 8 subtracted from 12 = 4

general form of the equation is y=a(x-4)^2 + k

when y= 50, x=16 and

50=a(144) + k

144a = 50-k

when y= 0, x= -4 or 8

0 = a(12-4)^2 + k

64a = -k

144a = (50+64a)

80a = 50

a =50/80 = 5/8

k=-64a = -64(5/8) = -40

Answer 2

We start writing the parabola as

y = a(x - 12)(x - -4) or a(x-12)(x+4)

As the parabola passes through (16,50)

a(16-12)(16+4) = 50

80a = 50

a= 5/8

y =5/8(x-12)(x+4) = 5/8(x^2-8x-48) = 5/8x^2 - 5x - 30

Answer 3