To translate the given statement into a quadratic equation, we start with "The product of 4 and a number squared". This can be expressed as \( 4x^2 \).
Next, we have "minus the product of 8 and that same number". This translates to \( -8x \).
Putting these two parts together, we get:
\[ 4x^2 - 8x \]
Finally, the statement says that this expression "is equal to 7". Thus, we can write the equation as:
\[ 4x^2 - 8x = 7 \]
This equation can be rearranged to standard quadratic form by moving 7 to the left side:
\[ 4x^2 - 8x - 7 = 0 \]
Now, looking at the options provided:
A) \( -4x^2 - 8x + 7 \)
B) \( 4x^2 - 8x + 7 \)
C) \( 4x^2 - 8x = 7 \)
D) \( -4x^2 + 8x = 7 \)
From our derived equation, option C is the one that matches the equation \( 4x^2 - 8x = 7 \).
Therefore, the correct answer is:
C) 4x^2 - 8x = 7.