Question

The curve y = ax^2 + b + c passes through the points (1, 8), (0, 5) and (3, 20). Find the values of a, b and c and hence the equation of the curve.

Answer 1

equation: y = x² + 2x + 5

Explanation:

y = ax² + bx + c

(y = ax^2 + b + c can't have a solution, must be y = ax^2 + bx + c)

passes through the points (1, 8), (0, 5) and (3, 20)

8 = a x 1² + b x 1 + c = a + b + c .......(1)

5 = a x 0² + b x 0 + c = c

20 = a x 3² + b x 3 + c = 9a + 3b + c .......(2)

8 = a + b + 5

a + b = 3 9a + 9b = 27

9a + 3b = 15

6b = 12

b = 2

a = 1

equation: y = x² + 2x + 5

Answer 2

Explanation:

y=ax²+bx+c

at (1,8)

8=a(1)²+b(1)+c

or

a+b+c=8 ...(1)

at (0,5)

5=a(0)²+b(0)+c

c=5

so a+b+5=8

a+b=8-5=3

a+b=3 ...(2)

at (3,20)

20=a(3)²+b(3)+c

20=9a+3b+5

9a+3b=20-5=15

3a+b=5 ...(3)

subtract (2) from (3)

3a+b-a-b=5-3

2a=2

a=2/2=1

from (2)

1+b=3

b=3-1=2

so y=x²+2x+5