Find the function with x-intercepts (-3,0) and (5,0), which also goes through the point (1,8). o f(x) = 0.5(x − 3)(x + 5)
o f(x) = -0.5(x − 3)(x+5)
o f(x) = 0.5(x + 3)(x - 5)
o f(x) = -0.5(x + 3)(x – 5)

f(x) = -0.5(x + 3)(x - 5)

Step-by-step explanation:

if the function intercepts the x-axis at x = -3 and x = 5, then

f(-3) = 0  and f(5) = 0

Therefore, we can say that (x + 3) and (x - 5) are factors as:

x + 3 = 0   ⇒ x = -3

x - 5 = 0   ⇒ x = 5

So  f(x) = a(x + 3)(x - 5)  where a is a constant

We are told that the function also passes through point (1, 8).

Substitute x = 1 into the function and equal it to 8:

Therefore, f(1) = a(1 + 3)(1 - 5) = 8

                               a x 4 x -4 = 8

                                   a x -16 = 8

                                            a = -0.5

Therefore, f(x) = -0.5(x + 3)(x - 5)