Question

if f(x)=ax^2+bx+c, find a, b, c given that f(1)=4, f(2)=13, f(-2)=1.​

Answer 1

Answer:

The values of a, b and c are 2, 3 and -1 respectively.

Given:

• f (x) = ax² + bx + c

• f (1) = 4, f (2) = 13 and f (-2) = 1

To find:

• The values of a, b and c.

Solution:

=> f (x) = ax² + bx + c

Substitute x = 1,

But, f (1) = 4

=> a (1)² + b (1) + c = 4

=> a + b + c = 4...(1)

Substitute x = 2,

But, f (2) = 13

=> a (2)² + b (2) + c = 13

=> 4a + 2b + c = 13...(2)

Substitute x = -2,

But, f (-2) = 1

=> a (-2)² + b (-2) + c = 1

=> 4a - 2b + c = 1...(3)

From equation (1), we get

>> c = 4 - a - b

Substitute c = 4 - a - b in equations (2) and (3), we get

=> 4a + 2b + 4 - a - b = 13

=> 3a + b = 9...(4)

And

=> 4a - 2b + 4 - a - b = 1

=> 3a - 3b = -3

=> a - b = -1...(5)

Add equations (4) and (5), we get

3a + b = 9

+

a - b = -1

_________

4a = 8

>> a = 2

Substitute a = 2 in equation (5), we get

>> 2 - b = -1

>> b = 3

Substitute the values of a and b in c = 4 - a - b, we get

>> c = 4 - 2 - 3

>> c = -1

The values of a, b and c are 2, 3 and -1 respectively.

Answer 2

Answer:

For f(x) = ax2 + bx + c, if f(1) = 8 and f(-1) = 4, find the value of a + c?

Get a global BA (H) in Liberal Arts, Sports, Design etc in India.

given f(x) = ax^2 + bx + c

(i) put x=1 , f(1) = a+b+c

but given that f(1) = 8 hence a+b+c = 8——————-(1)

(ii) put x=-1 , f(-1) = a-b+c

but given that f(-1) = 4 hence a-b+c = 4——————-(2)

consider (1) + (2) :- a+b+c + a-b+c = 8 + 4

2a + 2c = 12

2(a+c) =12

a+c = 6.