Question

Which of the following represents this function written in intercept form?

y = x^2 - 8x + 12
a) y = -(x + 3)(x - 4)
b) y = - (x + 2)(x - 6)
c) y = (x - 2)(x - 6)
d) y = - (x + 2)(x + 6)

Answer 1

c) y = (x - 2)(x - 6). The function y = x^2 - 8x + 12 in intercept form is c) y = (x - 2)(x - 6), which is the product of two binomials factored from the given quadratic function.

Step-by-step explanation:

The student is asking for the intercept form of the quadratic function y = x2 - 8x + 12. To find the intercept form, the quadratic needs to be factored. Given its standard form, y can be expressed as the product of two binomials where the factors of the constant term (12) combine to give the middle coefficient (-8) when factored properly.

The correct factoring of x2 - 8x + 12 is (x - 2)(x - 6). When multiplied, (x - 2)(x - 6) yields x2 - 8x + 12, which is identical to the original function. Hence the answer is c) y = (x - 2)(x - 6).