Question

Which function describes this graph?

Answer 1

C.) y = x² + 9x + 18

Explanation:

C.) is correct because the function has the accurate x-intercepts. X-intercepts are the x-values in which the line passes through the x-axis. We can prove this by setting the function equal to 0, factoring, then solving for "x". You can factor the function by asking yourself the question, "which two numbers multiply to 18 and add to 9?"

y = x² + 9x + 18 <----- Original function

0 = x² + 9x + 18 <----- Set the function equal to 0

0 = (x + 6)(x + 3) <----- Factor

0 = x + 6 0 = x + 3

-6 = x -3 = x

So, at (-3, 0) and (-6, 0), the function crosses the x-axis. This matches the given graph.

Answer 2

zeros: x=-3 x=-6

factors: x+3 x+6

`f(x) = (x + 3)(x + 6) \\ f(x) = x {}^(2) + 6x + 3x + 18 \\ f(x) = x {}^(2) + 9x + 18`

Option C