Question

Determine the equation of the graph, and select the correct answer below. parabolic function going down from the left and turning at the point negative three comma two and going up through the point zero comma twelve and continuing towards infinity Courtesy of Texas Instruments y = (x + 3)2 − 2 y = (x − 3)2 − 2 y = (x + 3)2 + 2 y = (x − 3)2 + 2

Answer 1

We have been given a graph and we are asked to find which of the given equations represent the graph.

Since we know that in vertex form of parabola $y=a(x-h)^{2}+k$, (h,k) is the vertex of parabola.  

We can see that our given equations are in vertex form. We are told that coordinates of vertex of given parabola are (-3,2).

Now let us compare our given examples with vertex form of parabola.

Upon looking at our options we can see that only option fits is:

$y=(x--3)^{2}+2$  

$y=(x+3)^{2}+2$  

Therefore, 3rd option is the correct choice.

Hope this helps.

Answer 2

the equation is y=(x-1)^2-3.

To check it, you can graph it on Desmos and compare the two.