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

−4x2+8x=7
negative 4 x squared plus 8 x is equal to 7

4x2−8x=7
4 x squared minus 8 x is equal to 7

−4x2−8x+7
negative 4 x squared minus 8 x plus 7

4x2−8x+7

Answer 1

To translate the given problem into a quadratic equation, let's first break down the statement:

"The product of 4 and a number squared" can be mathematically represented as \(4x^2\). "minus the product of 8 and that same number" would be \(-8x\). It is stated that this entire expression is equal to 7.

Putting it all together, you have:

\[4x^2 - 8x = 7\]

Now, if we rearrange this into standard quadratic form, we can express it as:

\[4x^2 - 8x - 7 = 0\]

But as per the options listed, the correct equivalent quadratic equation form is:

4x^2 - 8x = 7

So, the correct response is:

4x²−8x=7