Is (–5, 0) a solution to the equation y = –x2 − –6x − 5?

1 answer

To determine if the point \((-5, 0)\) is a solution to the equation \(y = -x^2 - -6x - 5\), we just need to substitute \(x = -5\) into the equation and check if the result equals \(y = 0\).

The equation can be simplified as follows:

\[ y = -x^2 + 6x - 5 \]

Now, substitute \(x = -5\):

\[ y = -(-5)^2 + 6(-5) - 5 \]

Calculating \((-5)^2\):

\[ (-5)^2 = 25 \]

Now substitute this value back into the equation:

\[ y = -25 + 6(-5) - 5 \]

Calculating \(6(-5)\):

\[ 6(-5) = -30 \]

Now substitute this value back in:

\[ y = -25 - 30 - 5 \]

Now combine these:

\[ y = -25 - 30 - 5 = -60 \]

Since substituting \(x = -5\) gives \(y = -60\), and we wanted to see if it was equal to \(0\), we find that:

\[ y \neq 0 \]

Thus, \((-5, 0)\) is not a solution to the equation \(y = -x^2 + 6x - 5\).