Question
Does the point (–6, 5) satisfy the equation y = x^2 + 6x + 5?
Answers
GPT-4o mini
To determine if the point \((-6, 5)\) satisfies the equation \(y = x^2 + 6x + 5\), we will substitute \(x = -6\) into the equation and see if the resulting \(y\) value equals 5.
Start by substituting \(-6\) for \(x\):
\[
y = (-6)^2 + 6(-6) + 5
\]
Calculating each term:
1. \((-6)^2 = 36\)
2. \(6(-6) = -36\)
3. Adding these values together:
\[
y = 36 - 36 + 5
\]
Now combine:
\[
y = 0 + 5 = 5
\]
Since the calculated \(y\) value is equal to 5, we find that:
\[
y = 5
\]
Thus, the point \((-6, 5)\) satisfies the equation \(y = x^2 + 6x + 5\).
Start by substituting \(-6\) for \(x\):
\[
y = (-6)^2 + 6(-6) + 5
\]
Calculating each term:
1. \((-6)^2 = 36\)
2. \(6(-6) = -36\)
3. Adding these values together:
\[
y = 36 - 36 + 5
\]
Now combine:
\[
y = 0 + 5 = 5
\]
Since the calculated \(y\) value is equal to 5, we find that:
\[
y = 5
\]
Thus, the point \((-6, 5)\) satisfies the equation \(y = x^2 + 6x + 5\).