Question

Use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.

Answer 1

Answer:

$y=-(x+1)^2+2$.

Step-by-step explanation:

This is a parabola so it's parent is $y=x^2$.

Let's described what happened to get from the parent to this.

The graph has been reflected so we will have $y=-x^2$.

The graph has been moved left 1 and up 2 so this gives us:

$y=-(x-(-1))^2+2$.

Simplifying this gives us $y=-(x+1)^2+2$.

Let's see if a few points we can identify can help confirm or convince you.

Some points I see that cross nicely are:

(-3,-2)

(-2,1)

(-1,2)

(0,1)

(1,-2)

Let's check them and see.

$y=-(x+1)^2+2$ with $(x,y)=(-3,-2)$:

$-2=-(-3+1)^2+2$

$-2=-(-2)^2+2$

$-2=-4+2$

$-2=-2$ is true so (-3,-2) does satisfy $y=-(x+1)^2+2$.

$y=-(x+1)^2+2$ with $(x,y)=(-2,1)$:

$1=-(-2+1)^2+2$

$1=-(-1)^2+2$

$1=-1+2$

$1=1$ is true so (-2,1) does satisfy $y=-(x+1)^2+2$.

$y=-(x+1)^2+2$ with $(x,y)=(-1,2)$:

$2=-(-1+1)^2+2$

$2=-(0)^2+2$

$2=0+2$

$2=2$ is true so (-1,2) does satisfy $y=-(x+1)^2+2$.

$y=-(x+1)^2+2$ with $(x,y)=(0,1)$:

$1=-(0+1)^2+2$

$1=-(1)^2+2$

$1=-1+2$

$1=-1$ is true so (0,1) does satisfy $y=-(x+1)^2+2$.

$y=-(x+1)^2+2$ with $(x,y)=(1,-2)$:

$-2=-(1+1)^2+2$

$-2=-(2)^2+2$

$-2=-4+2$

$-2=-2$ is true so (1,-2) does satisfy $y=-(x+1)^2+2$.

All the mentioned points satisfied our equation:

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