Answer :

Answer:

B

Step-by-step explanation:

Given the zeros , where the graph crosses the x- axis of a parabola , say x = a and x = b , then

the corresponding factors are (x - a) and (x - b)

The function is then the product of the factors, that is

y = a(x - a)(x - b) ← a is a multiplier

From the graph

The zeros are x = - 4 and x = 1 , then

(x - (- 4) ) and (x - 1) , that is (x + 4) and (x - 1) are the factors and

y = a(x + 4)(x - 1)

To find a, substitute the coordinates of any other point on the graph into the equation.

Using (0, 4 ) for x and y in the function

4 = a(0 + 4)(0 - 1) = a(4)(- 1) = - 4a ( divide both sides by - 4 )

- 1 = a

Then

y = - 1(x + 4)(x - 1) ← expand factors using FOIL

y = - (x² + 3x - 4 ) ← distribute parenthesis by - 1

y = - x² - 3x + 4