Question

Consider the quadratic function that has x-intercepts of -1 and -7 and passes through the point (-2,-20). What is the value of a in the factored form of this function?

a) 1
b) 2
c) 4
d) -2

Answer 1

The value of a in the factored form of the quadratic function with x-intercepts at -1 and -7, which also passes through the point (-2, -20), is 4.

Step-by-step explanation:

The student is asking to find the value of a in the factored form of a quadratic function with x-intercepts at -1 and -7 that also passes through the point (-2,-20). The factored form of this function would be a(x + 1)(x + 7). Since we know the function passes through the point (-2,-20), we can substitute these values into the equation to determine the value of a.

Plugging in the point, we get:

-20 = a(-2 + 1)(-2 + 7)

-20 = a(-1)(5)

-20 = -5a

To solve for a, divide both sides by -5:

a = -20 / -5

a = 4

Hence, the value of a is 4, which corresponds to option c).