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

Solution:

We have to find the coordinates of the vertex.

For any equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is y = x² + 4x + 10

Here, a = 1, b = 4 and c = 10

So, h = -4/2(1)

h = -4/2

h = -2

4ac = 4(1)(10)

4ac = 40

So, k = [40 - (4)²]/4(1)

k = (40 - 16)/4

k = 24/4

k = 6

Therefore, the coordinates of the vertex is (h, k) = (-2, 6).

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

Summary:

The coordinates of the vertex for f(x) = x² + 4x + 10 is (-2, 6).