Question

What are the x-intercept(s) of the graph of y + 6 = x2 − x?

Answer 1

set y=0 then solve the resulting equation for x: \(\large 0 + 6 = x^2 - x \)

Answer 2

First lets shift everything to one-side, so its nice to look at:

y + 6 = x^2 - x

y = x^2 - x - 6

Now, the x-intercepts are the values of (x) when (y) = 0. So lets set y = 0 and see what happens:

0 = x^2 - x - 6

Here, we will have to factor apart x^2 - x - 6. Which two numbers added together gives -1 and multiplied together give -6? Intuitively, I would say -3 and 2, hopefully you agree :)

0 = (x - 3)(x + 2)

so either (x - 3) = 0 and/or (x + 2) = 0, because if either one was 0, then the whole thing just becomes 0, since 0 times anything is 0.

(x - 3) = 0 and/or (x + 2) = 0

x - 3 = 0

x = 3

and/or

x + 2 = 0

x = -2

So your x-intercepts should be x = 3 and -2, when y = 0 or simply put: (3,0) and (-2,0).

Answer 3

thank you SO muchh<3