Question

Rewrite each equation in vertex form by completing the square. Then identify the vertex.

Answer 1

The vertex form of the given equation is f(x) = 3(x+3/2)²+(19/4) where vertex is (-3/2,19/4).

Explanation:

We have given a quadratic equation in standard form.

f(x)= 3x²+9x-2

We have to rewrite given equation in vertex form.

f (x) = a(x-h)²+k is vertex form of equation where (h,k) is vertex of equation.

We will use method of completing square to solve this.

Adding and subtracting (9/2)² to above equation, we have

f(x) = 3(x²+3x)-2

f(x) = 3(x²+3x+(3/2)² ) -2+3(3/2)²

f(x) = 3(x²+3x+(3/2)² ) -2+3(9/4)

f(x) = 3(x+3/2)²-2+27/4

f(x) = 3(x+3/2)²+(-8+27)/4

f(x) = 3(x+3/2)²+(19/4)

Hence, The vertex form of the given equation is f(x) = 3(x+3/2)²+(19/4) where vertex is (-3/2,19/4).

Answer 2

Vertex form;

`y = 3( {x + (3)/(2) })^(2) - (35)/(4)`

Vertex

`V( - (3)/(2) , - (35)/(4) )`

EXPLANATION

Given:

`f(x) = 3 {x}^(2) + 9x - 2`

We complete the square as follows:

`y = 3( {x}^(2) + 3x) - 2`

`y = 3( {x}^(2) + 3x + (9)/(4) ) - 2 - 3 * (9)/(4)`

The vertex form is:

`y = 3( {x + (3)/(2) })^(2) - (35)/(4)`

The vertex is

`V( - (3)/(2) , - (35)/(4) )`