Math Problem Statement
what is y=x²
Solution
The equation represents a parabola in the coordinate plane.
Key Features:
- Shape: It is a U-shaped curve that opens upwards.
- Vertex: The lowest point of the parabola is at the origin, .
- Axis of Symmetry: The line (the y-axis) is the axis of symmetry.
- Domain: The domain is all real numbers, .
- Range: The range is , as is always non-negative.
- Behavior:
- For , increases as increases.
- For , increases as increases.
Explanation of the Equation:
- The term means that the value of depends on the square of . Squaring any real number always results in a non-negative value.
Would you like a plot of this function? Or further exploration?
Related Questions:
- How do you find the vertex of a parabola in general form?
- How do transformations (e.g., ) change the graph of a parabola?
- How do you determine the focus and directrix of ?
- How does the graph change when you add a coefficient to , like ?
- What are the real-world applications of parabolic curves?
Tip:
To better understand the parabola, analyze its symmetry and how changes to affect .
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Quadratic Equations
Graphing
Formulas
y = x^2
Theorems
Properties of parabolas
Symmetry in quadratic functions
Suitable Grade Level
Grades 7-9