Question

The answer input says y = ____ x^2+ _____ x+ _______ for standard form for the quadratic equation with the roots -3 and 5 and a = 2

Answer 1

Given the roots of the quadratic equation to be

-3 and 5

This implies that x = -3 or x = 5

Equate the two roots to 0

Therefore, x + 3 = 0 or x - 5 = 0

(x + 3) (x - 5) = 0

Open the parentheses

`\begin{gathered} (x\text{ + 3) (x - 5) = 0} \\ x\cdot\text{ x - x}\cdot5\text{ + 3 }\cdot x\text{ + 3(-5) = 0} \\ x^2\text{ - 5x + 3x - 15 = 0} \\ x^2\text{ - 2x - 15 = 0} \\ \text{ Since the standard form of a quadratic equation is given as} \\ \text{y = ax}^2\text{ + bx + c} \\ \text{ and a = 2} \\ y=2x^2\text{ - 2x - 15 = 0} \end{gathered}`

y = 2x^2 + (-2)x + (-15)

The first blank is 2

The second blank is -2

The third blank is -15