Question

Which is true for all pairs of values in this table? x 0 1 2 3 y 2 3 6 11 a. y=x^2 + 3 b.y=x^2 + 1 c.y=x^2-1 d.y=x^2+2

Answer 1

The answer is D. y=2x+2

Answer 2

The answer would be: d.y=x^2+2
In this question, the table is made from an equation that follows y=ax^2+b. To find the equation, it would be easier to use x=0 so you can exclude the a value and find the value of b. From the description, you can find that x=0 will result in y=2. Then if you put it into the equation:
y=ax^2+b
2=a(0)^2+b
b=2

Now we need to find the value of a. You can do this by inserting any value of x and y beside x=0. Let's try to use x=2 and y=6
y=ax^2+b
6 =a(2)^2+2
6 =4a+2
4a =6-2
4a=4
a= 1

The equation would be:
y=ax^2+b
y=1x^2+2