Write a quadratic function in the form

Question

 f(x)=x^2+bx+c that has zeros 8 and 11.?

Answer 1

The function f(x) = x² + bx + c

y = x² + bx + c

Zeros are 8 and 11.

So it passes through (8, 0) and (11, 0).

Substitute For (x, y) = (8, 0) in y = x² + bx + c.

0 = (8)² + b(8) + c

64 + 8b + c = 0

8b + c = - 64 ---> (1)

Substitute For (x, y) = (11, 0) in y = x² + bx + c.

0 = (11)² + b(11) + c

121 + 11b + c = 0

11b + c = - 121 ---> (2)

Solve the equations (1) and (2)in elimination method.

To eliminate the c variable, subtract the equation (2) from (1).

(8b + c) - (11b + c) = - 64 - (- 121)

8b + c - 11b - c = - 64 + 121

- 3b = 57

b = - 57/3

b = - 19

Substitute the b value in equation (1).

8(- 19) + c = - 64

c = - 64 + 152

c = 88

Substitute b, c in f(x) = x² + bx + c.

Required equation is f(x) = x² - 19x + 88.