Question

What is the vertex of the graph of the quadratic function f(x)= x^{2} + 6x + 10?

Answer 1

vertex = (- 3, 1 )

Explanation:

given a quadratic in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

f(x) = x² + 6x + 10 ← is in standard form

with a = 1, b = 6 , then

x = -
`(6)/(2)` = - 3

substitute x = - 3 into f(x) for corresponding y- coordinate

f(- 3) = (- 3)² + 6(- 3) + 10 = 9 - 18 + 10 = 1

vertex = (- 3, 1 )