The x-intercepts are the solutions to the points (3, 0) and (-2, 0). We can rewrite them as factors.
x = 3 ⇒ x - 3 = 0
x = -2 ⇒ x + 2 = 0
The point (0, -3) is the y-intercept or the initial value to the quadratic equation. The quadratic equation is written in factored form such as y = a(x - 3)(x + 2). We need to find the value of 'a' by plugging in x = 0 and y = -3 to the quadratic equation.
a(0 - 3)(0 + 2) = -3 ⇒ a(-3)(2) = -3 ⇒ -6a = -3 ⇒ a = -3/-6 = 1/2
Our quadratic equation in factored form is y = 1/2(x - 3)(x + 2).
