What are the x-intercept(s) of the graph of $y + 12 = x^2 + x$ ?

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Answer 1 · 2017-06-11T21:41:57

See a solution process below:

To find the $x$ -intercepts we need to set $y$ to $0$ and solve for $x$ :

$y + 12 = x^2 + x$ becomes:

$0 + 12 = x^2 + x$

$12 - color(red)(12) = x^2 + x - color(red)(12)$

$0 = x^2 + x - 12$

$0 = (x + 4)(x - 3)$

Solution 1)

$x + 4 = 0$

$x + 4 - color(red)(4) = 0 - color(red)(4)$

$x + 0 = -4$

$x = -4$

Solution 2)

$x - 3 = 0$

$x - 3 + color(red)(3) = 0 + color(red)(3)$

$x - 0 = 3$

$x = 3$

The $x$ -intercepts are: $-4$ and $3$

Or

$(-4, 0)$ and $(3, 0)$

What are the x-intercept(s) of the graph of y + 12 = x^2 + xy + 12 = x^2 + x?