Select the quadratic equation that is equivalent to: The product of 4 and a number squared, minus the product of 8 and that same number is 7.

A) -4x^2 - 8x + 7
B) 4x^2 - 8x + 7
C) 4x^2 - 8x = 7
D) -4x^2 + 8x = 7

1 answer

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.