Find the equation of the axis of symmetry of the following parabola algebraically.

y, equals, minus, x, squared, plus, 8, x

*y*=−*x*2+8*x*

The equation of a parabola in standard form is given by:

\[
y = ax^2 + bx + c
\]

The axis of symmetry of a parabola can be found using the formula:

\[
x = \frac{-b}{2a}
\]

### Step-by-step solution:

1. The given equation is:

\[
y = -x^2 + 8x
\]

2. Identify the coefficients:
   - \(a = -1\) (the coefficient of \(x^2\))
   - \(b = 8\) (the coefficient of \(x\))
   - There is no constant term, so \(c = 0\).

3. Apply the axis of symmetry formula:

\[
x = \frac{-b}{2a} = \frac{-8}{2(-1)} = \frac{-8}{-2} = 4
\]

### Final answer:
The equation of the axis of symmetry is \(x = 4\).

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. How would the axis of symmetry change if the equation was \(y = -2x^2 + 8x\)?
2. What is the vertex of the parabola described by \(y = -x^2 + 8x\)?
3. How does the sign of \(a\) affect the direction of the parabola?
4. How would you graph the equation \(y = -x^2 + 8x\)?
5. What happens to the axis of symmetry when the constant term \(c\) is added?

**Tip:** The axis of symmetry always passes through the vertex of the parabola.

Find the equation of the axis of symmetry of the following parabola algebraically.
y = -x^2 + 8x

Learn how to find the equation of the axis of symmetry for the quadratic parabola y = -x^2 + 8x. This problem demonstrates how to apply the axis of symmetry formula and is perfect for students in Grades 8-10.

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