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The equation given is:

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

This is a transformed version of the parent function \( y = x^2 \), which is a standard parabola opening upwards. Here’s how each part of the equation affects the graph:

1. **Horizontal Shift**: The \((x + 2)\) inside the square indicates a horizontal shift. Since it’s \((x + 2)\), the graph shifts **2 units to the left**.
2. **Vertical Shift**: The \(+ 5\) outside the square moves the graph **5 units up**.

As a result, the vertex of the parabola, which is normally at \((0, 0)\) for \(y = x^2\), is now at \((-2, 5)\).

The transformed graph should show a parabola opening upwards with its vertex at \((-2, 5)\).

Would you like a further breakdown of these transformations or have any specific questions?

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Here are some related questions:
1. What is the effect of a negative sign in front of the squared term, such as in \(y = -(x+2)^2 + 5\)?
2. How would the graph change if we had \((x - 2)^2 + 5\) instead?
3. What happens if we add a coefficient to the squared term, like \(y = 2(x+2)^2 + 5\)?
4. How does the vertex form of a parabola help in quickly identifying transformations?
5. Can we rewrite \(y = (x + 2)^2 + 5\) in standard form?

**Tip:** When graphing transformations, start with the vertex shift and then apply other transformations like stretching or reflecting.

Graph the equation y = (x + 2)^2 + 5 by transforming the given graph of the parent function.

Learn how to graph the transformed quadratic equation y = (x + 2)^2 + 5, using vertex form transformations. Understand the horizontal and vertical shifts from the parent function y = x^2. This problem covers key concepts in graph transformations and quadratic functions, ideal for students in Grades 9-10.

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