The quadratic function given in the image is:

$f(x) = -2(x + 4)^2 + 3$

This equation is in vertex form, which is:

$f(x) = a(x - h)^2 + k$

In this form, $(h, k)$ represents the coordinates of the vertex of the parabola.

Comparing the given equation:

• $(x + 4)^2$ means $h = -4$ (since it's $x - (-4)$).
• The constant $+3$ indicates $k = 3$.

Thus, the vertex of the parabola is:

$(-4, 3)$

Would you like more details on this, or do you have any further questions?

Here are 5 related questions you could explore:

1. How does changing the value of $a$ affect the shape of a parabola?
2. What does the vertex form of a quadratic equation tell us about the graph?
3. How would the vertex change if the equation were $f(x) = -2(x - 4)^2 + 3$?
4. How do we convert a quadratic equation in standard form to vertex form?
5. How does the sign of $a$ (positive or negative) influence the direction of the parabola?

Tip: The value of $a$ determines the "width" and direction (upward or downward) of the parabola.