Question

HELP PLEASE

problems 11 through 17​

Answer 1

Part 11) The vertex is the point (4,32)

Part 12) The vertex is the point (1,-5)

Part 13) The vertex is the point (-2,5)

Part 14) The vertex is the point (-1,-1)

Part 15) The vertex is the point (1,8)

Part 16) The vertex is the point (3,-26)

Part 17) The vertex is the point (-5,-32)

Explanation:

Part 11) we have

`y=-x^2+8x+16`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=-x^2+8x+16`

Factor -1

`y=-(x^2-8x)+16`

Complete the square

`y=-(x^2-8x+16)+16+16`

`y=-(x^2-8x+16)+32`

Rewrite as perfect squares

`y=-(x-4)^2+32`

The vertex is the point (4,32)

Part 12) we have

`y=3x^2-6x-2`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=3x^2-6x-2`

Factor 3

`y=3(x^2-2x)-2`

Complete the square

`y=3(x^2-2x+1)-2-3`

`y=3(x^2-2x+1)-5`

Rewrite as perfect squares

`y=3(x-1)^2-5`

The vertex is the point (1,-5)

Part 13) we have

`y=-2x^2-8x-3`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=-2x^2-8x-3`

Factor -2

`y=-2(x^2+4x)-3`

Complete the square

`y=-2(x^2+4x+4)-3+8`

`y=-2(x^2+4x+4)+5`

Rewrite as perfect squares

`y=-2(x+2)^2+5`

The vertex is the point (-2,5)

Part 14) we have

`y=2x^2+4x+1`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=2x^2+4x+1`

Factor 2

`y=2(x^2+2x)+1`

Complete the square

`y=2(x^2+2x+1)+1-2`

`y=2(x^2+2x+1)-1`

Rewrite as perfect squares

`y=2(x+1)^2-1`

The vertex is the point (-1,-1)

Part 15) we have

`y=-5x^2+10x+3`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=-5x^2+10x+3`

Factor -5

`y=-5(x^2-2x)+3`

Complete the square

`y=-5(x^2-2x+1)+3+5`

`y=-5(x^2-2x+1)+8`

Rewrite as perfect squares

`y=-5(x-1)^2+8`

The vertex is the point (1,8)

Part 16) we have

`y=3x^2-18x+1`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=3x^2-18x+1`

Factor 3

`y=3(x^2-6x)+1`

Complete the square

`y=3(x^2-6x+9)+1-27`

`y=3(x^2-6x+9)-26`

Rewrite as perfect squares

`y=3(x-3)^2-26`

The vertex is the point (3,-26)

Part 17) we have

`y=x^2+10x-7`

we know that

The quadratic equation written in vertex form is equal to

`y=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex

Convert to vertex form

`y=x^2+10x-7`

Complete the square

`y=(x^2+10x+25)-7-25`

`y=(x^2+10x+25)-32`

Rewrite as perfect squares

`y=(x+5)^2-32`

The vertex is the point (-5,-32)