Question

Which of the following functions have the same y-intercept as the function below? SELECT ALL THAT APPLY.

f(x)=x^2-7x+12

A. f(x)=(x-3)(x-4)

B. f(x)= (x-2)(x-5)

C. f(x)= x^2-7x+6

D. f(x)= x^2-8x+12

E. f(x)= (x-1)^2+12

F. f(x)= (x-2)^2+8

Answer 1

Option A. when you use foil on it, it turns into the starting equation

Answer 2

The functions that will have the same intercept $f(x)=x^2-7x+12$ are options A, option D and option F.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The y-intercept of the given function can be written as,

$f(x)=x^2-7x+12\\\\f(0)=(0)^2-7(0)+12\\\\y = 12$

In order to find the y-intercept of the given function, we need to put the value of the x as zero in all the functions and check if the value of the function is the same or not.

A.)

$f(x)=(x-3)(x-4)\\\\f(0)=(0-3)(0-4)= 12$

B.)

$f(x)= (x-2)(x-5)\\\\f(0)= (0-2)(0-5) = 10$

C.)

$f(x)= x^2-7x+6\\\\ f(0)= (0)^2-7(0)+6=6$

D.)

$f(x)= x^2-8x+12\\\\ f(0)= (0)^2-8(0)+12 = 12$

E.)

$f(x)= (x-1)^2+12\\\\f(0)= (0-1)^2+12=13$

F.)

$f(x)= (x-2)^2+8\\\\f(0)= (0-2)^2+8 = 12$

Hence, the functions that will have the same intercept $f(x)=x^2-7x+12$ are options A, option D and option F.

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