Question

Vertex of f(x)=-x^2+2x-9

Answer 1

vertex = (1, - 8 )

Explanation:

given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

f(x) = - x² + 2x - 9 ← is in standard form

with a = - 1 and b = 2 , then

`x_(vertex)` = -
`(2)/(2(-1))` = -
`(2)/(-2)` = - (- 1) = 1

substitute x = 1 into f(x) for corresponding y- coordinate

f(1) = - 1² + 2(1) - 9 = - 1 + 2 - 9 = - 8

coordinates of vertex = (1, - 8 )