Find the equation in standard form of the parabola that passes through the points (0, 6),
(-3, 15), and (-6, 6).

Step-by-step explanation:

When parabola f(x) = ax² + bx + c passes through point (x₁, y₁) that means if x=x₁ then f(x)=f(x₁)=y₁

(0, 6) ⇒   6=a·0²+b·0+c    ⇒   c=6

f(x) = ax² + bx + 6

(-3, 15)  ⇒  15 = a(-3)² + b(-3) +6   ⇒  9a - 3b = 9 ⇒

                                                      ⇒ 3a - b = 3  ⇒ b = 3a - 3

(-6, 6)  ⇒  6 = a(-6)² + b(-6) +6  ⇒ 36a - 6b = 0  ⇒

                                                      ⇒  6a - b = 0   ⇒ b = 6a

6a = 3a - 3   ⇒  3a = - 3  ⇒  a = -1

b = 6(-1) = -6

So the equation:

                         f(x) = (-1)x² + (-6)x + 6

                         f(x) = -x² - 6x + 6

answer: i'm great at algebra

~coco

step-by-step explanation:

i use my brain for prombles like this maybe you could try it

step-by-step explanation: