# Determine the quadratic function y=x^2-mx+8 if f(3)=4.

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Given f(x)= x^2 - mx + 8

We need to find the value of m such that f(3) = 3

We will substitute with x= 3

==> f(3)= 3^2 - 3*m + 8 = 4

==> 9 - 3m + 8 = 4

We will combine like terms.

==> -3m = 4 -8 -9

==> -3m = -13

Now we will divide by -3

==> m = -13/-3 = 13/3

Then the value of m is 13/3

**Then the quadratic function is : **

**f(x)= x^2 - 13 x /3+ 8**

The quadratic function is f(x) = y = x^2 - mx + 8.

We know that f(3) = 4

=> 3^2 - m*3 + 8 = 4

=> 9 - 3m + 8 = 4

=> -3m = -13

=> m = 13/3

**This gives the quadratic function as y = x^2 - (13/3)x + 8**

We'll substitute x by 3 in the expression of the given function f(x):

f(3) = 3^2-m*3+8

f(3) = 9 - 3m + 8

We'll combine like terms and we'll get:

f(3) = 17 - 3m

From enunciation, we know that f(3)=4=>17 - 3m = 4 => 3m = 13

We'll divide by -2:

m = 13/3

**The quadratic function is: f(x)=x^2 - 13x/3 + 8.**