Question

Write an equation in intercept form of the parabola that passes through the point (1,32) and has x-intercepts −7 and 3?

Answer 1

Given that the parabola passes through points (1,32) and the x-intercepts are (-7,0) and (3,0)
thus the equation will be as follows:
y=a(x-k)(x-h)
where:
(x-k) and (x-h) are the factors:
thus
y=a(x+7)(x-3)
y=a(x^2+4x-21)
But, when x=1, y=32
plugging this in the equation we get:
32=a(1^2+4(1)-21)
32=a(1+4-21)
32=-16a
hence:
a=-2
thus the eqiation will be:
y=-2(x^2+4x-21)
hence the equation is:
y=-2x^2-8x+42