𝑓 of 𝑥 equals 𝑥 cubed minus two 𝑥 squared. Circle the value of 𝑓 of negative four. Is it negative 32, 48, negative 96, or 32?
The value of 𝑓 of negative four is the output when we input negative four for 𝑥: negative four cubed minus two times negative four squared. Negative four cubed equals negative 64. Negative four squared equals 16. Bring down the rest of the equation. Negative two times 16 equals negative 32. Bring down the negative 64. And now we have negative 64 minus 32, which equals negative 96.
When working through problems like this, we have to make sure we’re careful with our signs. Negative four cubed is negative four times negative four times negative four, which results in a negative number, while negative four squared is negative four times negative four and results in positive 16. Then we’re multiplying negative two times a positive 16, which gives us negative 32. And negative 64 minus 32 is negative 96.