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

(3, –25)
(–3, –25)
(3, 29)
(–3, 29)

Keywords

vertex, vertical parabola

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex

If -----> the parabola open upward (vertex is a minimum)

If -----> the parabola open downward (vertex is a maximum)

In this problem we have

so

the parabola open downward (vertex is a maximum)

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

The vertex is the point

therefore

the answer is the option

Option C - (3,29)

Step-by-step explanation:

Given : Equation

To find : The vertex of the equation

Solution :

The general form of the equation through which we get the vertex of the equation is

Where, (h,k) are the vertex of the equation

So, first we have to convert the equation into the general form

Let g(x)=y

Applying completing the square

i.e, subtract and add square of half of 6 = 9

Comparing with the general form,

a= -3 , h=3 and k=29

Therefore, (h,k)=(3,29) are the vertex of the given equation.

Hence, Option C is correct.

54.864 meters

step-by-step explanation: