Write an equation of the parabola in intercept form that passes through (-18, 72) with x-intercepts of -16 and -2 .

Answer 1

A way to approach this problem is to view the x-intercepts as solutions to a one-variable quadratic equation.

If x = -16 or x = -2, then x + 16 = 0 or x + 2 = 0.

If these are multiplied together, we get y = (x + 16)(x + 2). However if we plug in -18 for x, we get

y = (-18 + 16)(-18 + 2) for y = (-2)(-16) = 32. We needed y to equal 72 when x = -18.

If we multiply the expression by a constant k, the x-intercepts are unaffected, and we can get it to go through the desired point (-18, 72).

k(-18 + 16)(-18 + 2) = 72

32k = 72

k = 9/4 = 2.25

So now the equation is y = 2.25(x² + 18x + 32) or

y = 2.25x² + 40.5x + 72.