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(1 point)

Question

Responses

4x^2−8x+7
4 x squared minus 8 x plus 7

4x^2−8x=7
4 x squared minus 8 x is equal to 7

−4x^2+8x=7
negative 4 x squared plus 8 x is equal to 7

−4x^2−8x+7

Answer 1

To translate the given statement into a quadratic equation, let's break it down. The statement says:

"The product of 4 and a number squared, minus the product of 8 and that same number is 7."

We can express this mathematically as follows:

1. Let the number be represented as \( x \).
2. The product of 4 and a number squared is \( 4x^2 \).
3. The product of 8 and that same number is \( 8x \).
4. Therefore, the equation becomes: \[ 4x^2 - 8x = 7 \]

Now this equation can be rearranged as: \[ 4x^2 - 8x - 7 = 0 \]

This means that the equivalent form to choose from the options provided is:

4x^2−8x=7

So the correct response is: 4x^2−8x=7