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