https://file.aiquickdraw.com/mathbot/file/17266195180074bmtvpct.jpg

The equation presented in the image is:

\[
y^2 - 10y - x + 24 = 0
\]

This represents a sideways parabola (since the equation involves \(y^2\) instead of \(x^2\)). To sketch the graph, we first rewrite the equation in a form that is easier to analyze. Let's complete the square for the \(y\)-terms.

1. Rearrange the equation:
   \[
   y^2 - 10y = x - 24
   \]

2. Complete the square on the left-hand side:
   \[
   y^2 - 10y + 25 = x - 24 + 25
   \]
   \[
   (y - 5)^2 = x + 1
   \]

Now, this is a standard form for a sideways parabola, where:

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

In this case, \(h = -1\) and \(k = 5\), and the parabola opens to the right. The vertex is at \((-1, 5)\), and the axis of symmetry is \(y = 5\).

### Steps to Graph:
1. **Vertex**: The vertex is at \((-1, 5)\).
2. **Direction**: Since the equation has a positive coefficient in front of \(x\), the parabola opens to the right.
3. **Shape**: The parabola will be symmetric about \(y = 5\).

Would you like more details on how to plot this or a step-by-step walkthrough on the solution?

Here are 5 related questions:
1. What is the general form of a sideways parabola?
2. How do you complete the square for quadratic terms?
3. What are the steps to identify the vertex of a parabola?
4. How does the direction of the parabola change when the coefficient of \(x\) is negative?
5. How can you find the focus and directrix of this parabola?

**Tip**: Completing the square is a useful technique for rewriting quadratic equations in a form that reveals important features like the vertex of a parabola!

Trazar el gráfico de la parábola: y^2 - 10y - x + 24 = 0

Learn how to graph the sideways parabola represented by the equation y^2 - 10y - x + 24 = 0. This guide covers the steps to complete the square and identify the vertex, axis of symmetry, and direction of the parabola. Suitable for students in Grades 9-12.

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