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) = (x+7/2)²+(-61/4) where vertex is (-7/2,-61/4).

Explanation:

We have given a quadratic equation in standard form.

f (x)= x²+7x-3

We have to rewrite given equation in vertex form.

y = 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 (7/2)² to above equation, we have

f(x) = x²+7x-3+(7/2)²-(7/2)²

f(x) = x²+7x+(7/2)²-3-(7/2)²

f(x) = (x+7/2)²-3-49/4

f(x) = (x+7/2)²+(-12-49)/4

f(x) = (x+7/2)²+(-61/4)

Hence, The vertex form of the given equation is f(x) = (x+7/2)²+(-61/4) where vertex is (-7/2,-61/4).

Answer 2

Vertex form

`f(x) = {( x + (7)/(2)) }^(2) - (61)/(4)`

Vertex:

`V( - (7)/(2) , - (6 1)/(4) )`

EXPLANATION

The given function is

`f(x) = {x}^(2) + 7x - 3`

Add and subtract the square of half the coefficient of x.

`f(x) = {x}^(2) + 7x + ( { (7)/(2) })^(2) - 3 + ( { (7)/(2) })^(2)`

The vertex form is

`f(x) = {( x + (7)/(2)) }^(2) - (61)/(4)`

The vertex is

`V( - (7)/(2) , - (6 1)/(4) )`