Question

To solve the equation −x − 3 = x2 − 2x− 15, you could graph of the following system.

y = −x − 3
y = x2 − 2x − 15

Use the graph of this system to identify all solutions of −x − 3 = x2 − 2x − 15.


-7

-3

0

4
On a coordinate plane, a parabola and a line are shown. The parabola opens up, has a vertex at (1, negative 16), and goes through (negative 3, 0) and (5, 0). The line has a negative slope and goes through (negative 3, 0), (0, negative 3), and (4, negative 7).

Answer 1

The solutions are x = −3 and x = 4.

Reason: intersections of y = −x − 3 and y = x^2 − 2x − 15 occur where the graphs meet, at (−3, 0) and (4, −7). Algebraically: x^2 − 2x − 15 = −x − 3 ⇒ x^2 − x − 12 = 0 ⇒ (x + 3)(x − 4) = 0.