Question

Can you please help me on this four questions please!

Please answer all portion of the question
Please show your work
35 points!!

Answer 1

1.
`d)y=x^2+2`

2.
`b)y=2x^2`

3.
`c)y=-x^2`

4.
`c)y=(1)/(2)x^2`

Step-by-step explanation:

1. Start with the pair (0,2)

Just because it is quick to substitute x = 0 mentally and get the answer by inspection. You will quickly notices that a), b) and c) do not match:

`a)y=2x^2=2(0)^2=2(0)=0\implies (0,0)wrong`

`b)y=(x-3)^2=(0-3)^2=(-3)^2=9\implies (0,9)wrong`

`c)y=x^2-3=(0)^2-3=0-3=-3\implies (0,-3)wrong`

`d)y=x^2+2=(0)^2+2=0+2=2\implies (0,2)\checkmark`

Thus, the answer is d)

2. Try b) y = 2x² for every point

`(2,8)\implies x=2\implies y=2(2)^2=8\checkmark\\\\(-2,8)\implies x=-2\implies y=2(-2)^2=8\checkmark\\\\(4,3)\implies x=4\implies y=2(4)^2=32\checkmark\\\\(-3,18)\implies x=-3\implies y=2(-3)^2=18\checkmark`

Thus, b) y=2x² is the correct equation.

3. Since every y is negative the only possible answer is c) y = -x²

Proove it:

`x=4\implies y=-(4)^2=-16\checkmark\\\\x=-4\imples y=-(-4)^2=-16\checkmark\\\\x=3\implies y=-(3)^2=-9\checkmark\\\\x=-3\impliesy=-(-3)^2=-9\checkmark`

4. Try c) y = (1/2)x²

`(4,8)\implies x=4\implies y=(1)/(2) (4)^2=8\checkmark\\ \\ (2,2)\implies x=2\implies y=(1)/(2) (2)^2=2\checkmark\\\\(6,18)\implies x=6\implies y=(1)/(2) (6)^2=18\checkmark\\ \\ (-4,8)\implies x=-4\implies y=(1)/(2) (-4)^2=8\checkmark`

Thus, c) y = (1/2)x²