We are going to evaluate the function f of x equals 2 x squared minus x plus 3 at x equals 4. This means we need to find the output value of the function when we substitute 4 for x.
To evaluate f of 4, we substitute 4 for every instance of x in the function. This gives us f of 4 equals 2 times 4 squared minus 4 plus 3.
We now follow the order of operations, often remembered by PEMDAS or BODMAS. First, we calculate the exponent: 4 squared equals 16. Next, we perform the multiplication: 2 times 16 equals 32. Finally, we combine the terms: 32 minus 4 plus 3.
Now we perform the final arithmetic. First, 32 minus 4 equals 28. Then, 28 plus 3 equals 31. Therefore, f of 4 equals 31.
To summarize, we evaluated f of x equals 2 x squared minus x plus 3 at x equals 4. We substituted 4 for x, followed the order of operations, and found that f of 4 equals 31. This means that when x is 4, the y-coordinate on the graph of the function is 31, corresponding to the point (4, 31).