Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or - 1. There may be more than one correct answer.

The y-intercept is

(0, 9).

The x-intercepts are

(-3, 0), (3, 0).

Degree is 2.

End behavior: as

x → - ∞,

f (x) → - ∞,

as

x → ∞,

f (x) → - ∞.

y = - x² + 9

the x-intercepts are x = - 3 and x = 3 hence the factors are

(x + 3) and (x - 3)

polynomial is the product of its factors

y = a (x - 3) (x + 3) ← (a is a multiplier)

from the end behaviour the parabola opens down and is a maximum and so the value of a is negative

y = - (x - 3) (x+3) = - (x² - 9) = - x² + 9