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

Question

asked Jun 12, 2020 89.7k views

2 Answers

Jack Chorley · Answer 1 · 2020-06-18T08:28:13+0000

The equation which is correct for the given function is:

D.
y+2=2(x+3)^2

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:

$y=(-3+4)(-3+2)\\\\y=1* (-1)\\\\y=-1\\eq -2$

Hence, option: A is incorrect.

B)

y=x^2+3x-2

when x= -2 we have:

$y=(-2)^2+3* (-2)-2\\\\y=4-6-2\\\\y=-4\\eq 0$

Hence, option: B is incorrect.

C)

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

when x= -2 we have:

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

$y=-4\\eq 0$

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.