Question

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

O (2,6)
O (-2, 2)
O (2, 2)
O (-2,6)

Answer 1

(X-2)^2 +6
a=1
h=2
k=6
Vertex(h,k)
(2,6)

Answer 2

Hi there!

`\huge\boxed{-2, 6}`

Convert f(x) = x² + 4x + 10 into Vertex form by completing the square:

0 = x² + 4x + 10

Use the first two terms to create a perfect square trinomial. Remember to add the third term to both sides:

0 + 4 = (x² + 4x + 4) + 10

Rewrite the trinomial as a square binomial:

4 = (x + 2)² + 10

Subtract 4 from both sides:

0 = (x + 2)² + 6

The equation in vertex form is:

f(x) = (x + 2)² + 6

A parabola in vertex form is f(x) = a(b(x-h))² + k where:

h = x-coordinate of vertex

k = y-coordinate of vertex

In this instance, h = -2 and k = 6, so:

The vertex is at (-2, 6)