Question

Which of the following is the correct equation for this function?
A. y= (x+4)(x+2)
B. y=x^2+ 3x – 2
C. y+ 2 = – 2(x+3)^2
D. y+ 2 = 2(x+3)^2

Answer 1

Answer:

The equation which is correct for the given function is:

           D.   $y+2=2(x+3)^2$

Step-by-step explanation:

By looking at the graph we observe that the graph of the function passes through the point (-4,0) , (-2,0)  , (-3,-2)

A)

         $y=(x+4)(x+2)$

when x= -3 we have:

$y=(-3+4)(-3+2)\\\\y=1\times (-1)\\\\y=-1\neq -2$

Hence, option: A is incorrect.

B)

     $y=x^2+3x-2$

when x= -2 we have:

$y=(-2)^2+3\times (-2)-2\\\\y=4-6-2\\\\y=-4\neq 0$

Hence, option: B is incorrect.

C)

    $y+2=-2(x+3)^2$

when x= -2 we have:

$y+2=-2(-2+3)^2\\\\y+2=-2$

$y=-4\neq 0$

Hence, option: C is incorrect.

D)

   $y+2=2(x+3)^2$

We see that the graph of this equation matches the given graph of the function.