To find the vertex of a quadratic function, we first need to rewrite the given expression in a more standard quadratic form.

Given expression:

$-2^2 + 8$

This can be interpreted as: $y = -2x^2 + 8$ where $a = -2$, $b = 0$, and $c = 8$, which is a quadratic equation in standard form $y = ax^2 + bx + c$.

Steps to find the vertex:

1. Identify the coefficients:

   • $a = -2$
   • $b = 0$
   • $c = 8$

2. Find the x-coordinate of the vertex: The formula for the x-coordinate of the vertex is: $x_{\text{vertex}} = \frac{-b}{2a}$ Since $b = 0$, this simplifies to: $x_{\text{vertex}} = 0$

3. Find the y-coordinate of the vertex: To find the y-coordinate, substitute $x_{\text{vertex}} = 0$ into the original equation: $y = -2(0)^2 + 8 = 8$

Thus, the vertex of the function $y = -2x^2 + 8$ is at: $(0, 8)$

Would you like more details on how to graph this or further explanation on quadratic functions?

Related Questions:

1. How do you graph a quadratic function?
2. What does the vertex of a quadratic function represent?
3. How do you find the axis of symmetry of a quadratic function?
4. How does the value of "a" affect the shape of the parabola?
5. What is the difference between standard form and vertex form of a quadratic?

Tip:

In a quadratic function, the value of "a" determines if the parabola opens upwards (if $a > 0$) or downwards (if $a < 0$).