The equation \( y = x^2 - 10x + 25 \) is a quadratic equation. Let's break it down:

1. **Standard Form**: The equation is already in the form \( y = ax^2 + bx + c \), where \( a = 1 \), \( b = -10 \), and \( c = 25 \).

2. **Factored Form**: We can factor this quadratic expression:
   \[
   y = (x - 5)^2
   \]
   This is because \( x^2 - 10x + 25 \) is a perfect square trinomial.

3. **Vertex Form**: The vertex form of the quadratic is \( y = (x - 5)^2 \), which shows that the vertex of the parabola is at \( (5, 0) \).

4. **Graphical Interpretation**: The equation \( y = (x - 5)^2 \) represents a parabola that opens upwards, with its vertex at \( (5, 0) \). The parabola touches the x-axis at \( x = 5 \), meaning it has a **single root**.

Would you like more details on any of these steps?

Here are 5 related questions:
1. How do you find the axis of symmetry for the quadratic equation?
2. Can you explain how to complete the square to convert to vertex form?
3. What is the discriminant, and how does it apply to this equation?
4. How would the graph change if the coefficient of \( x^2 \) was different?
5. How can this quadratic equation be used to solve real-life problems?

**Tip**: When factoring quadratic expressions, always check if it forms a perfect square trinomial for easier simplification.

Learn how to solve and factor the quadratic equation y = x^2 - 10x + 25. This tutorial covers key algebraic concepts like factoring perfect square trinomials, vertex form, and graphical interpretations of quadratics. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation