Question

Does (2, –48) make the equation y = –6x^2 − –87x + –50 true?

Answer 1

To determine whether the point \((2, -48)\) satisfies the equation \(y = -6x^2 - 87x - 50\), we will substitute \(x = 2\) into the equation and see if it produces \(y = -48\).

Substituting \(x = 2\):

\[
y = -6(2^2) - 87(2) - 50
\]

Calculating \(2^2\):

\[
2^2 = 4
\]

Now substituting this into the equation:

\[
y = -6(4) - 87(2) - 50
\]

Calculating \(-6(4)\):

\[
-6(4) = -24
\]

Calculating \(-87(2)\):

\[
-87(2) = -174
\]

Now substituting these values back into the equation:

\[
y = -24 - 174 - 50
\]

Now, we can combine the terms:

\[
y = -24 - 174 = -198
\]

Then add \(-50\):

\[
y = -198 - 50 = -248
\]

The calculation shows:

\[
y = -248
\]

Now we check if \(-248\) is equal to \(-48\):

\(-248 \neq -48\)

Thus, the point \((2, -48)\) does **not** satisfy the equation \(y = -6x^2 - 87x - 50\).