To determine if \((-3, 5)\) is a solution to the equation \(y = x^2 + 8x - 6\), we can substitute \(x = -3\) into the equation and check if the resulting value of \(y\) equals 5.

Given equation:  
\[ y = x^2 + 8x - 6 \]

Substitute \(x = -3\):
\[
y = (-3)^2 + 8(-3) - 6
\]
\[
y = 9 - 24 - 6
\]
\[
y = -21
\]

The calculated value of \(y\) is \(-21\), but the given \(y\)-coordinate is 5. Therefore, \((-3, 5)\) is **not** a solution to the equation \(y = x^2 + 8x - 6\).

Would you like more details or have any further questions?

Here are some related questions:
1. How can you determine if a point is a solution to a quadratic equation?
2. What does the graph of \(y = x^2 + 8x - 6\) look like?
3. How can you find the vertex of a quadratic equation?
4. How do you find the roots of \(y = x^2 + 8x - 6\)?
5. What is the axis of symmetry for the quadratic equation \(y = x^2 + 8x - 6\)?

**Tip:** When checking if a point is a solution to an equation, always substitute both coordinates to see if the equation holds true!

Determine if the point (-3, 5) is a solution to the quadratic equation y = x^2 + 8x - 6 by substituting the x-coordinate into the equation and solving for y. Explore key algebraic concepts and the substitution method, suitable for students in Grades 7-9.

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