What is the vertex of g(x) = -3x² + 18x + 2?

Solution:

We know that vertex form of a parabola is is

y = a (x - h)² + k

Where (h, k) is the vertex

g(x) = -3x² + 18x + 2 [Given]

It can be written by completing the square as:

y = -3x² + 18x + 2

=-3(x² + 6x)+ 2

= -3(x² + 6x+ 9)+ 2 + 27

y = - 3(x - 3)² + 29

Comparing this with the standard form

a = -3

h = 3

k = 29

Therefore, the vertex is (3, 29).

What is the vertex of g(x) = -3x² + 18x + 2?

Summary:

The vertex of g(x) = -3x² + 18x + 2 is (3, 29).