For the function `f(x)=5x^2-7x`, what is the value of `f(-3)`?

Options

A. `-66`
B. `-24`
C. 24
D. 66

Answer

To find the value of \( f(-3) \) for the function \( f(x) = 5x^2 - 7x \), we will follow these steps:

### Step 1: Substitute \(-3\) for \(x\) in the function
We start with the function:
\[ f(x) = 5x^2 - 7x \]
Now, we substitute \(-3\) in place of \(x\):
\[ f(-3) = 5(-3)^2 - 7(-3) \]

### Step 2: Calculate \((-3)^2\)
Next, we calculate \((-3)^2\):
\[ (-3)^2 = 9 \]
So, we can rewrite the function:
\[ f(-3) = 5(9) - 7(-3) \]

### Step 3: Multiply \(5\) by \(9\)
Now, we multiply \(5\) by \(9\):
\[ 5(9) = 45 \]
Thus, we have:
\[ f(-3) = 45 - 7(-3) \]

### Step 4: Calculate \(-7(-3)\)
Next, we calculate \(-7(-3)\):
\[ -7(-3) = 21 \]
So, we can now rewrite the function:
\[ f(-3) = 45 + 21 \]

### Step 5: Add \(45\) and \(21\)
Finally, we add \(45\) and \(21\):
\[ 45 + 21 = 66 \]

### Final Answer
Thus, the value of \( f(-3) \) is:
\[ \boxed{66} \]