Find the formula in standard form y=ax^2+bx+c

Question

for a quadratic that has roots at x = -9 and x = 7, and has leading coefficient of 1.

Answer 1

To solve this, we use the factored form of a quadratic equation: f(x) = a(x-p)(x-q) where (x-p) and (x-q) are factors in the equation and a is the leading coefficient. To get the factors, we need to use the roots given to solve for the factors. Essentially, we need to reorder the roots to get all values on one side and a zero on the other side of the equal sign.

For x = -9, we convert it to x + 9 = 0 (by adding 9 to both sides). We convert x = 7 to x - 7 = 0 by subtracting 7 from both sides. The non-zero side of these equations form the factors (x-p) and (x-q). Then, we plug the solutions back into the original factored form of the quadratic equation. Remember, a = 1 (leading coefficient), (x-p) = (x+9) and (x-q) = (x-7).

y = a(x-p)(x-q)

y = (1)(x+9)(x-7) (Next, multiply these binomials using FOIL, First, Outer, Inner, Last. The leading 1 can go away here.)

y = (x²-7x+9x-56) (Here, just combine like terms to get the final solution.)

Hope this helps!