Question

Write an equation in factored form given the "a" value is -3 and the x-intercepts are -2 and 5. (Hint: write your equation with no spaces. Write the term with "2" first)

Answer 1

-3(x-5)(x+2)

Explanation:

the generic form of a second degree equation is:

y = ax^2 + bx + c

with "a" = -3, we have y = -3x^2 + bx + c

for y=0 (x-intercepts), we have x = -2 and x = 5, so:

1: 0 = -3*(-2)^2 + b*(-2) + c

-12 -2b + c = 0

-2b + c = 12 (eq1)

2: 0 = -3*5^2 + b*5 + c

-75 + 5b + c = 0

5b + c = 75 (eq2)

doing (eq2) - (eq1), we have:

7b = 63 -> b = 9

using b = 9 in (eq1), we have:

-18 + c = 12 -> c = 30

so, the equation is y = -3x2 + 9x + 30

in factored form: y = -3(x2 - 3x - 10) = -3(x-5)(x+2)