# Let `f(x) = x^2 - 3x - 7` . Find `f(-3)` .

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### 6 Answers

To solve this problem, we simply substitute -3 for x in every term for f(x) in the following way:

`f(-3) = (-3)^2 - 3(-3) -7`

Let's simplify. Remember, when you square a negative number, you get a positive result:

`f(-3) = 9 - (-9)-7`

Now, we're subtracting a negative number. This equates to adding a positive number! Let's continue:

`f(-3) = 9 + 9 - 7`

Now, we just add and subtract:

`f(-3) = 18 - 7 = 11`

Therefore, f(-3) = 11. And you're done!

I hope that helps. I could see in this question how you might get caught up in the signs of each term (whether they're negative or positive, whether you add or subtract, or what-have you). Just remember that you multiply first, then add or subtract. Also, if you have difficulty conceptualizing the negatives and positives, you might find it helpful to just memorize the rules associated with them:

Multiplication:

positive * positive = positive

negative * negative = positive

positive * negative = negative

negative * positive = negative

Addition/Subtraction:

Number + positive = number - negative

Number - positive = number + negative

Hopefully that works for you!

**Sources:**

This is a simple substitution problem:

Let . Find .

. Find

substitute the Xs with -3

f(-3) = -3^2 -3(-3) - 7

simplify

f(-3) = 9 + 9 -7

combine terms

f(-3) = 11

You would simply substitute -3 for x

IT would then become:

f(-3)=(-3)^2-3(-3)-7

f(-3)=(9)+(9)-7

f(-3)=18-7

f(-3)=11

Sorry correction the second to last step should read 18-7

F (x)= X^2 -3x-7, and f (-3)

So you just substitute -3 for the x giving you

(-3^2)-3 (-3)-7

9+9-7

18_7

=11