y = −x2 + 18x − 45. (a) Find the vertex and (b) factor and state the roots

Answer 1

To find the vertex, use x = -b/a

For this equation b = 18 and a = -1

x = -18/-1

x = 18

Substitute 1 into the given equation to find the value of y for the coordinates of the vertex.

Beware of the first term. where -x^2.

That means square the x value and then change the sign. Be very careful when entering into a calculator.

For factoring, I find it easier to divide through by -1 when the first term is negative.

x^2 - 18x + 45. = 0

Factor and solve for x. Your answers can be checked by plugging them into the original equation.

Answer 2

y = -x² + 18x - 45

y = -(x - 3)(x - 15)

Zeros: 3, 5

Vertex at x = -18 / 2(-1), or 9

(9, 36)