Question

PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)

Answer 1

(- 1, 2)

Explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

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

f(x) = x² + 2x + 3 ← is in standard form

with a = 1 and b = 2, hence

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

Substitute x = - 1 into f(x) for corresponding value of y

f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

vertex = (- 1, 2 )