Question

Determine a quadratic function 'f' given by :
f(x) = ax² + bx + c if f(0)=6 , f(2)=11 and f(-3)=6

I want the solving of the three equations to be elaborated

Answer 1

this is your required solution

Answer 2

Answer:

Step-by-step explanation:

Given

f(x) = ax² + bx+ c

If f(0) = 6

This means we have to put x=0 in the given equation,

f(0) = a(0)²+b(0)+ c = 6

or, c=6

If f(2)=11

put x=2 in the given equation,

f(2)= a(2)²+ b(2)+ 6= 11

4a²+ 2b = 11-6

4a²+ 2b =5.........(i)

If f(-3)=6

Put x= -3 in the given equation,

f(-3)= a(-3)²+ b(-3) + 6= 6

a(-3)²+ b(-3) = 0,

9a -3b= 0

9a = 3b

3a = b.......(ii)

Put value of b = 3a

4a²+ 2b =5

4a² + 2(3a) = 5

4a²+ 6a-5 = 0

On solving for a, and b

You will get the quadratic equation 'f'