Question

Can i have some help? i'm kinda desperate AND please NO fake answers don't answer if you will give a fake answer

btw if you want an extra 50 points or more you could maybe help with another question i asked recently on my profile as not all of them received applicable answers

Answer 1

Explanation:

Vertex form is:
`a(x-h)^2+k`

a)
`a(x+2)^2+3=y`

To find a, plug (-4,1) in for x and y.

`a(-4+2)^2+3=1`

`4a=-2`

`a=-1/2`

so a) is
`(-1)/(2) (x+2)^2+3`

b) .... I'm not sure what the second coordinate is.

c)
`a(x+2)^2-3`

Plug in (-5,6) for x and y.

`6=a(-5+2)^2-3`

`9=9a`

`a=1`

so c) is
`(x+2)^2-3`

d)
`a(x+2)^2+5`

Plug (1,-4) in for x and y.

`-4=a(1+2)^2+5`

`-9=9a`

`a=-1`

so d) is
`-(x+2)^2+5`

Answer 2

`\textsf{(a)}\quad y=-(1)/(2)(x+2)^2+3`

`\textsf{(b)}\quad y=a(x+1)^2-1`

`\textsf{(c)}\quad y=(x+2)^2-3`

`\textsf{(d)}\quad y=-(x+2)^2+5`

Explanation:

Vertex form

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

where (h, k) is the vertex

-------------------------------------------------------------------------------------------

Part (a)

Given: vertex at (-2, 3) passes through (-4 ,1)

Substituting the given vertex into the equation:

`\implies y=a(x-(-2))^2+3`

`\implies y=a(x+2)^2+3`

Substitute the given point into the equation to find a:

`\implies 1=a(-4+2)^2+3`

`\implies 1=4a+3`

`\implies a=-(1)/(2)`

Substitute the found value of a to form the final equation:

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

-------------------------------------------------------------------------------------------

Part (b)

Given: vertex at (-1, -1) passes through ?)

Substituting the given vertex into the equation:

`\implies y=a(x-(-1))^2+(-1)`

`\implies y=a(x+1)^2-1`

Substitute the given point into the equation to find a:

**no point given**

-------------------------------------------------------------------------------------------

Part (c)

Given: vertex at (-2, -3) passes through (-5, 6)

Substituting the given vertex into the equation:

`\implies y=a(x-(-2))^2+(-3)`

`\implies y=a(x+2)^2-3`

Substitute the given point into the equation to find a:

`\implies 6=a(-5+2)^2-3`

`\implies 6=9a-3`

`\implies a=1`

Substitute the given point into the equation to find a:

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

-------------------------------------------------------------------------------------------

Part (d)

Given: vertex at (-2, 5) passes through (1, -4)

Substituting the given vertex into the equation:

`\implies y=a(x-(-2))^2+5`

`\implies y=a(x+2)^2+5`

Substitute the given point into the equation to find a:

`\implies -4=a(1+2)^2+5`

`\implies -4=9a+5`

`\implies a=-1`

Substitute the given point into the equation to find a:

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