Evaluate f of 4 if f of x equals negative 2 x squared plus 5x minus 8.

To evaluate ( f(4) ) for the function ( f(x) = -2x^2 + 5x - 8 ), you start by substituting ( x ) with 4 in the equation.

First, calculate ( 4^2 ):

[

4^2 = 16.

]

Then, substitute 4 into the function:

[

f(4) = -2(16) + 5(4) - 8.

]

Now do the multiplications:

[

-2(16) = -32,

]

and

[

5(4) = 20.

]

Insert these values back into the equation:

[

f(4) = -32 + 20 - 8.

]

Next, perform the addition and subtraction:

[

-32 + 20 = -12,

]

Then,

[

-12 - 8 = -20.

]

Therefore, the evaluation yields ( f(4) = -20 ).

This confirms that the value of ( f(4) ) is indeed (-20).