Math Problem Statement
y=x2+3
Solution
The equation you've provided is:
This represents a quadratic function. Let's break it down:
- Parabola: The graph of this equation is a parabola, opening upwards, since the coefficient of is positive.
- Vertex: The vertex of the parabola is at , because the constant term shifts the graph upwards by 3 units.
- Axis of symmetry: The axis of symmetry is the vertical line , which passes through the vertex.
- Y-intercept: The y-intercept is at , because when , .
- X-intercepts: There are no real x-intercepts, as the equation does not have real solutions (it only has complex solutions).
Would you like more details or have any questions?
Here are five questions related to this:
- How would the graph change if we modified the equation to ?
- What are the complex solutions to the equation ?
- How does the value of the constant term affect the graph of a quadratic equation?
- Can you describe how to find the axis of symmetry for any quadratic function?
- What is the general form of a quadratic equation?
Tip: For quadratic equations, the vertex form is useful for identifying the vertex and transformations of the graph easily!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Parabolas
Formulas
Standard form of a quadratic equation: y = ax^2 + bx + c
Axis of symmetry: x = -b/2a
Theorems
No real solutions theorem for x^2 + c = 0 when c > 0
Vertex form transformation theorem
Suitable Grade Level
Grades 9-10