Question

Does (–1, 9) make the equation y = 4x3 + 8x2 − –6x − –7 true?

Answer 1

To determine if the point \((-1, 9)\) satisfies the equation \(y = 4x^3 + 8x^2 - 6x - 7\), we can substitute \(x = -1\) into the equation and see if the resulting \(y\) value is equal to 9.

Starting with the equation:

\[
y = 4x^3 + 8x^2 - 6x - 7
\]

Substituting \(x = -1\):

\[
y = 4(-1)^3 + 8(-1)^2 - 6(-1) - 7
\]

Calculating each term:

1. \(4(-1)^3 = 4(-1) = -4\)
2. \(8(-1)^2 = 8(1) = 8\)
3. \(-6(-1) = 6\)
4. The constant term is \(-7\)

Now we can combine these results:

\[
y = -4 + 8 + 6 - 7
\]

Calculating step-by-step:

1. \(-4 + 8 = 4\)
2. \(4 + 6 = 10\)
3. \(10 - 7 = 3\)

So, we find that:

\[
y = 3
\]

Since the point is \((-1, 9)\) and we calculated \(y\) to be 3, the equation does not hold true, as \(3 \neq 9\).

Thus, the point \((-1, 9)\) does **not** make the equation true.