Consider the following function.

a(x)=−(x+2)2+3
a
(
x
)
=
−
(
x
+
2
)
2
+
3
Step 1 of 4 :  Find the vertex.

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.

Consider the following function: a(x) = -(x + 2)^2 + 3. Step 1 of 4: Find the vertex.

Learn how to find the vertex of the quadratic function a(x) = -(x + 2)^2 + 3, using vertex form. This tutorial covers key algebra concepts like vertex form and properties of parabolas, making it suitable for Grades 9-10.

Math Problem Statement

a(x)=−(x+2)2+3 a ( x )

Solution

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