Question

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

Answer 1

ANSWER

Vertex form;

$y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}$

Vertex

$V( - \frac{3}{2} , - \frac{35}{4} )$

EXPLANATION

Given:

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

We complete the square as follows:

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

$y = 3( {x}^{2} + 3x + \frac{9}{4} ) - 2 - 3 \times \frac{9}{4}$

The vertex form is:

$y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}$

The vertex is

$V( - \frac{3}{2} , - \frac{35}{4} )$

Answer 2

Answer:

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

Step-by-step 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).