Question

Write the quadratic equation whose roots are 6 and -6, and whose leading coefficient is 2.

(Use the letter x to represent the variable.)

Answer 1

`2x^2-6`

Explanation:

If a quadratic equation has a root at a certain point, the x value must equal. zero. If we want to have the function reach 6 and -6 as roots:

x = 6

x - 6 = 0

x = -6

x + 6 = 0

Combining the two we get (x+6)(x-6) which will give us a quadratic equation.

Expanding:
`x^2-6x+6x-6 = x^2-6`

The leading coefficient is the number before the variable with the highest power, which is 2:
`2x^2-6`