Ariana Moon 123

Question

The points (0,3), (1,4),(2,7), and (3,12) are on the graph of a function. Which equation represents that function?

Answer 1

y=Ax^3+Bx^2+Cx+D

(0,3) --> D=3 --> y=Ax^3+Bx^2+Cx+3

(1,4) --> A+B+C+3 = 4

A+B+C = 1

(2,7) --> 8A + 4B + 2C + 3 = 7

8A + 4B + 2C = 4

4A+2B+C = 2

(3,12) --> 27A + 9B + 3C + 3 = 12

27A + 9B + 3C = 9

9A + 3B + C = 3

3x3 system is:

A + B + C = 1

4A + 2B + C = 2

9A + 3B + C = 3

Eq2 - Eq1: 3A + B = 1

Eq3 - Eq2: 5A + B = 1

2A = 0

A=0

B=1

C=0

y= 0x^3 + 1* x^2 + 0x + 3 = x^2+3

Answer 2

Roughly plotting the points, looks like a parabola.

y=ax²+bx+c

y(0) = 0+0+c=3 --> c = 3

y(1) = a+b+3 = 4 --> a+b=1 (Eq1)

y(2) = 4a+2b +3 = 7 --> 4a+2b=4 ->2a+b=2 (Eq2)

Subtract Eq1 from Eq2, a = 1 and b = 0

y = x²+3

y(3) = 9+3 = 12 So it checks out