Question

Go from roots to factors, multiply the factors by FOIL technique, and write the answer in Standard Form (y=ax^2+bx+c): x=-12 and x=-5

Answer 1

To find the quadratic equation with roots x=-12 and x=-5, we convert the roots to factors (x+12) and (x+5), apply the FOIL technique, and simplify to obtain the Standard Form of the quadratic equation: y = x² + 17x + 60.

Step-by-step explanation:

For roots x=-12 and x=-5, we convert these roots into factor form: (x - (-12)) and (x - (-5)), which simplifies to (x + 12) and (x + 5) respectively. To find the quadratic equation in Standard Form, we need to apply the FOIL technique (First, Outer, Inner, Last):

• First: x * x = x²
• Outer: x * 5 = 5x
• Inner: 12 * x = 12x
• Last: 12 * 5 = 60

Combining these terms, we have x² + 5x + 12x + 60. Simplifying, we get x² + 17x + 60. So the quadratic equation in Standard Form with these roots is y = x² + 17x + 60.