Determine the equation of the parabola with x-intercepts -4 and 3, that passes through (2,7).

Answer 1

Since the x-intercepts are -4 and 3, the parabola has the form:

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

To find the value of a, we can substitute the given point (2,7) into the equation:

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

7 = a(6)(-1)

7 = -6a

Dividing both sides by -6:

a = -7/6

So the equation of the parabola is:

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