Write an equation for a parabola with x-intercepts (-1,0) and (3,0) which passes through the point (1,-16)

Answer 1

To find an equation for the given parabola, we can start by using the intercept form of a parabola equation: y = a(x - h)(x - k), where (h, k) is the vertex of the parabola.

Given that the parabola has the x-intercepts (-1,0) and (3,0), we know that the factors (x - h) are (x + 1) and (x - 3).

So far, our equation is y = a(x + 1)(x - 3).

We also know that the parabola passes through the point (1, -16). Plugging in the x and y coordinates of this point into the equation, we get:
-16 = a(1 + 1)(1 - 3)
-16 = a(2)(-2)
-16 = a(-4)
-16 = -4a

Solving for a, we divide both sides of the equation by -4:
a = -16 / -4
a = 4

Now that we have the value for a, we can substitute it into the quadratic equation:
y = 4(x + 1)(x - 3)

Thus, the equation for the given parabola is y = 4(x + 1)(x - 3).