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

Step-by-step 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 $\frac{-1}{2} (x+2)^2+3$

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

Answer:

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

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

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

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

Step-by-step explanation:

Vertex form

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

where (h, k) is the vertex

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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:

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

$\implies 1=4a+3$

$\implies a=-\dfrac{1}{2}$

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

$y=-\dfrac{1}{2}(x+2)^2+3$

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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**

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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:

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