Question

Write the equation in standard form y = ax^2 + bx + c if the roots ar 3 and - 6 and it passes through (2, -8)

A. y = x^2 - 3x - 18

B. y = x^2 + 3x + 18

C. y = x^2 + 3x - 18

D. y = x^2 - 3x - 18

Answer 1

To determine the quadratic equation in standard form with roots 3 and -6, we first find the factors of the equation:

(x - 3)(x + 6) = 0

Expanding this expression gives:

x^2 + 6x - 3x - 18 = 0
x^2 + 3x - 18 = 0

Now, since it passes through the point (2, -8), we can substitute these values into the equation:

-8 = 2^2 + 3(2) - 18
-8 = 4 + 6 - 18
-8 = -8

Therefore, the correct equation in standard form is:

y = x^2 + 3x - 18

So, the answer is:

C. y = x^2 + 3x - 18