Question

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) → −∞.

Answer 1

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