Final answer:
The equation for a parabola with x-intercepts (-1,0) and (5,0) that passes through the point (4,-25) is y = 5(x + 1)(x - 5).
Step-by-step explanation:
To write an equation for a parabola with x-intercepts (-1,0) and (5,0) which passes through the point (4,-25), we can start with the form y = a(x - r)(x - s), where r and s are the x-intercepts of the parabola.
Given the x-intercepts (-1,0) and (5,0), our equation becomes:
y = a(x + 1)(x - 5)
To find the value of a, we will substitute the coordinates of the point (4, -25) into the equation and solve for a:
-25 = a(4 + 1)(4 - 5)
By simplifying and solving, we get:
-25 = a(5)(-1)
a = 5
So, the equation of the parabola is:
y = 5(x + 1)(x - 5)