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

[tex]Rewrite each equation in vertex form by completing the square. then identify the vertex.[/tex]

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

[tex]Rewrite each equation in vertex form by completing the square. then identify the vertex.[/tex]

ANSWER

Vertex form:

[tex]y = 2( {x - 4)}^{2} - 27[/tex]

Vertex:

V(4,-27)

EXPLANATION

The given function is

[tex]y = 2 {x}^{2} - 16x + 5[/tex]

Complete the square as follows:

[tex]y = 2( {x}^{2} - 8x) + 5[/tex]

[tex]y = 2( {x}^{2} - 8x + 16) + 5 - 2 \times 16[/tex]

[tex]y = 2( {x - 4)}^{2} + 5 - 32[/tex]

The vertex form is:

[tex]y = 2( {x - 4)}^{2} - 27[/tex]

The vertex is:

V(4,-27)

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

Step-by-step 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

Vertex form;

[tex]y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}[/tex]

Vertex

[tex]V( - \frac{3}{2} , - \frac{35}{4} )[/tex]

EXPLANATION

Given:

[tex]f(x) = 3 {x}^{2} + 9x - 2[/tex]

We complete the square as follows:

[tex]y = 3( {x}^{2} + 3x) - 2[/tex]

[tex]y = 3( {x}^{2} + 3x + \frac{9}{4} ) - 2 - 3 \times \frac{9}{4}[/tex]

The vertex form is:

[tex]y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}[/tex]

The vertex is

[tex]V( - \frac{3}{2} , - \frac{35}{4} )[/tex]

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).

The vertex form of the given equation is y = (x+4)²-11 where vertex is (-4,-11).

Step-by-step explanation:

We have given a quadratic equation in standard form.

y = x²+8x+5

We have to rewrite given equation in vertex form.

y = (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 (4)² to above equation, we have

y = x²+8x+5 +(4)²-(4)²

y = x²+8x+(4)²+5-(4)²

y = (x)²+2(x)(4)+(4)²+5-16

y = (x+4)²-11

Hence, the vertex form of the given equation is y = (x+4)²-11 where vertex is (-4,-11).

ANSWER

Vertex form:

[tex]y = ( {x + 4)}^{2} - 11[/tex]

Vertex

V(-4,-11)

EXPLANATION

The given expression is

[tex]y = {x}^{2} + 8x + 5[/tex]

We complete the square to get the vertex form.

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

[tex]y = {x}^{2} + 8x + 16 + 5 - 16[/tex]

[tex]y = ( {x + 4)}^{2} - 11[/tex]

The vertex is

V(-4,-11)

The vertex form of the given equation is f(x) = 2(x-4)²+(-27) where vertex is (4,-27).

Step-by-step explanation:

We have given a quadratic equation in standard form.

y= 2x²-16x+5

We have to rewrite given equation in vertex form.

y = (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.

y = 2(x²-8x)+5

Adding and subtracting (-4)² to above equation, we have

y = 2(x²-8x+(-4)²)+5-2(-4)²

y = 2(x-4)²+5-2(16)

y = 2(x-4)²+ 5 -32

y = 2(x-4)²-27

Hence, The vertex form of the given equation is f(x) = 2(x-4)²+(-27) where vertex is (4,-27).

ANSWER

Vertex form

[tex]f(x) = {( x + \frac{7}{2}) }^{2} - \frac{61}{4}[/tex]

Vertex:

[tex]V( - \frac{7}{2} , - \frac{6 1}{4} )[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 7x - 3[/tex]

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

[tex]f(x) = {x}^{2} + 7x + ( { \frac{7}{2} })^{2} - 3 + ( { \frac{7}{2} })^{2}[/tex]

The vertex form is

[tex]f(x) = {( x + \frac{7}{2}) }^{2} - \frac{61}{4}[/tex]

The vertex is

[tex]V( - \frac{7}{2} , - \frac{6 1}{4} )[/tex]