The vertex of the parabola defined by the equation, y = 5(x + 2)2 - 4 is

To find the vertex of the parabola defined by the equation \( y = 5(x + 2)^2 - 4 \), you can use the standard form of a parabola's equation, which is:

\[
y = a(x - h)^2 + k
\]

In this form:
- \( (h, k) \) represents the vertex of the parabola.

The given equation is already in this form:

\[
y = 5(x + 2)^2 - 4
\]

Here:
- \( h = -2 \) (because the equation has \( (x + 2) \), which is equivalent to \( (x - (-2)) \)),
- \( k = -4 \).

Therefore, the vertex of the parabola is:

\[
\text{Vertex} = (-2, -4)
\]

### Do you want details or have any questions?

Here are 5 related questions to explore:
1. How can you determine if the parabola opens upwards or downwards from the equation?
2. How do you find the axis of symmetry for this parabola?
3. How does changing the coefficient \( a \) affect the shape of the parabola?
4. What is the significance of the vertex in the context of real-world problems?
5. How do you convert a quadratic equation from standard form to vertex form?

**Tip:** When identifying the vertex, remember that the sign inside the parentheses for \( h \) is opposite to the value of \( h \) in the vertex.

Learn how to find the vertex of the parabola defined by the equation y = 5(x + 2)^2 - 4 with a detailed step-by-step solution. Understand the standard form of a quadratic equation and its application to determine the vertex. Suitable for high school students.

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