If the points (3,17) and (4,29) are on the graph of the quadratic function y=2x^2+bx+c,

Question

what are the values of b and c?

Answer 1

The quadratic function y = 2x² + bx + c

And it passes through (3, 17) and (4, 29)

Substitute for (x ,y) = (3, 17) in y = 2x² + bx + c.

17 = 2(3)² + b(3) + c

17 = 18 + 3b + c

3b + c = 17 - 18

3b + c = - 1 ----> (1)

 

Substitute for (x ,y) = (4, 29) in y = 2x² + bx + c.

29 = 2(4)² + b(4) + c

29 = 32 + 4b + c

29 - 32 = 4b + c

4b + c = - 3 ---> (2)

 

Now solve the equations (1) and (2).

From (1) , c = - 1 + 3b

Substitute c = - 1 + 3b in equation (2).

4b +( - 1 + 3b) = - 3

7b - 1 + 3b = - 3

10b = - 3 + 1

10b = - 2

b = -2/10

b = -1/5

Substitute b  = -1/5 in equation (1).

3(-1/5) + c = - 1

(- 3/5) + c = - 1

c = - 1 + (3/5)

c = (- 5 + 3)/5

c = - 2/5

Substitute b and c in y = 2x² + bx + c

And the equation is y = 2x² + (- x/5) + (-2/5).

The values : b = -1/5 and c = -2/5.