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)

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

Step-by-step 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)