Answer:
1. [tex]d)y=x^2+2[/tex]
2. [tex]b)y=2x^2[/tex]
3. [tex]c)y=-x^2[/tex]
4. [tex]c)y=\dfrac{1}{2}x^2[/tex]
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:
[tex]a)y=2x^2=2(0)^2=2(0)=0\implies (0,0)wrong[/tex]
[tex]b)y=(x-3)^2=(0-3)^2=(-3)^2=9\implies (0,9)wrong[/tex]
[tex]c)y=x^2-3=(0)^2-3=0-3=-3\implies (0,-3)wrong[/tex]
[tex]d)y=x^2+2=(0)^2+2=0+2=2\implies (0,2)\checkmark[/tex]
Thus, the answer is d)
2. Try b) y = 2x² for every point
[tex](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[/tex]
Thus, b) y=2x² is the correct equation.
3. Since every y is negative the only possible answer is c) y = -x²
Proove it:
[tex]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[/tex]
4. Try c) y = (1/2)x²
[tex](4,8)\implies x=4\implies y=\frac{1}{2} (4)^2=8\checkmark\\ \\ (2,2)\implies x=2\implies y=\frac{1}{2} (2)^2=2\checkmark\\\\(6,18)\implies x=6\implies y=\frac{1}{2} (6)^2=18\checkmark\\ \\ (-4,8)\implies x=-4\implies y=\frac{1}{2} (-4)^2=8\checkmark[/tex]
Thus, c) y = (1/2)x²
