Answer:
[tex]f(x) = -4(x+7)(x+1)[/tex]
Step-by-step explanation:
Quadratic equation:
A quadratic equation, with roots(x-intercepts) at [tex]x_1[/tex] and [tex]x_2[/tex], and leading coefficient a, is given by:
[tex]f(x) = a(x - x_1)(x - x_2)[/tex]
Has x-intercepts of -7 and -1
So [tex]x_1 = -7, x_2 = -1[/tex]. Thus
[tex]f(x) = a(x - (-7))(x - (-1)) = a(x+7)(x+1)[/tex]
Passes through the point (-4,36).
This means that when [tex]x = -4, y = 36[/tex], and we use this to find the leading coefficient.
[tex]36 = a(-4+7)(-4+1)[/tex]
[tex]a(3)(-3) = 36[/tex]
[tex]-9a = 36[/tex]
[tex]a = -\frac{36}{9}[/tex]
[tex]a = -4[/tex]
So
[tex]f(x) = -4(x+7)(x+1)[/tex]
