Determine the equation of the Parabola

Determine the equation of the Parabola with the following:

The x-intercepts are -4 and 3, and the curve passes through the point (2,7)

Could you also explain how you got this? Thanks!

The x-intercepts are the points where y = 0. Therefore, the equation for the parabola must be of the form

y = a(x - (-4))(x - 3) = a(x + 4)(x - 3)

for some number a.

If the parabola passes through a point, the point's coordinates must satisfy the parabola's equation.

7 = a(2 + 4)(2 - 3) = -6a
-7/6 = a

Thus, an equation for the parabola is

y = (-7/6)(x + 4)(x - 3)

If you need the equation in another form, that's up to you.