a(x)=−(x+2)2+3 a ( x )

The function is given as:

$a(x) = -(x+2)^2 + 3$

This is a quadratic function in vertex form:

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

Where $(h, k)$ is the vertex of the parabola.

In this case, we have:

$a(x) = -(x + 2)^2 + 3$

• The expression $(x + 2)$ can be rewritten as $(x - (-2))$, which means $h = -2$.
• The constant term $+3$ gives $k = 3$.

Thus, the vertex of the function is $(-2, 3)$.

The vertex is $(-2, 3)$.

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

Here are some related questions for deeper understanding:

1. What is the axis of symmetry for this function?
2. How does the graph behave as $x \to \infty$ or $x \to -\infty$?
3. What is the maximum value of the function?
4. How does the transformation affect the shape of the graph?
5. Can you rewrite the function in standard form?

Tip: The sign of the coefficient of $(x - h)^2$ determines whether the parabola opens upwards or downwards.