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

The answer is D. y=2x+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