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
