The points (0, 2), (1, 3), (2, 6), and (3, 11) are on the graph of a function. Which of the following equations represents that function?

Question

1. A. h(x) = 2x²
2. B. h(x) = x² + 2
3. C. h(x) = 0.5x² +1.5
4. D. h(x) = x + 2

Answer 1

Looking at the data, you can see that when x = 0, h(x) = 2. This disqualifies A and C. Looking at the y points, you can see that they don't increase linearly; so, that suggests the quadratic function. As a check, substitute the x values of 2 and 6 into equation C; this gives the given values of 6 and 11 for h(x).

Answer 2

The points (0, 2), (1, 3), (2, 6), and (3, 11) are on the graph of a function. Which of the following equations represents that function?

1.  A. h(x) = 2x²
2.  B. h(x) = x² + 2
3. C. h(x) = 0.5x² +1.5
4. D. h(x) = x + 2

Let's take the first point (x,y) where x = 0 and y = 2

note: another name for h(x) is y

plug x = 0 into A. y = 2(0)^2 = 0, That does not work. since y needs to be 2

plug x = 0 into B. y = 0^2 + 2 = 2 that works

plug x = 0 into C. y = 0.5(0)^2 + 1.5 = 1.5 that does not work. since y needs to be 2

plug x = 0 into D. y = 0 + 2 that works

so be are down to B or D

take the next point (1,3)

plug x = 1 into B and D. they both work.

take the next point (2,6).

plus x = 2 into B and D. only B works.

confirm the last point (3, 11) works for B and it does

B is the answer.