Answer:
y = -x^2 - 4x + 5.
Step-by-step explanation:
As it passes through the point (1, 0) it must have one zero of value x = 1 so it has a factor (x - 1).
so y = a(x - 1)(x - b) where a and b are constants.,
Now we substitute the points (-2, 9) and (-4, 5) into this equation:
9 = a(-2 - 1)(-2 - b)
9 = a(-3)(-2- b)
9 = 6a + 3ab -----------(1)
5 = a(-4 - 1)(-4 - b)
5 = -5a(-4 - b)
5 = 20a + 5ab............(2)
Multiply (1) by 5 and (2) by 3
45 = 30x + 15ab
15 = 60a + 15ab
Subtracting these 2 equations:
30 = -30a
a = -1.
Substituting a = -1 in equation (1):
9 = 6(-1) + 3(-1)b
3b = -6 - 9
b = -15/3
b = -5.
So the equation is y = -(x - 1)(x + 5).
In standard form
y = -(x^2 + 4x - 5)
y = -x^2 - 4x + 5.
