Math Problem Statement
Y= (x+5)2 +9
Solution
The given equation is:
This is a quadratic function in the standard form of a parabola, , where:
- (the coefficient of ),
- (the x-coordinate of the vertex, derived from ),
- (the y-coordinate of the vertex).
Key points:
- Vertex: The vertex is at . This is the point where the parabola reaches its minimum value since , which means it opens upwards.
- Axis of symmetry: The axis of symmetry is the vertical line .
- Direction: The parabola opens upwards because .
Let me know if you'd like more details about this equation, or if you have any specific questions!
Follow-up questions:
- How can we find the x-intercepts of this equation?
- What happens if we change the value of ?
- How do you graph a quadratic function from its vertex form?
- How do you calculate the maximum or minimum value of a quadratic function?
- Can you solve this equation for a specific value of ?
Tip:
When working with vertex form , you can directly identify the vertex, axis of symmetry, and direction of the parabola, making it easier to sketch the graph!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex Form of a Parabola
Formulas
Vertex form of a quadratic function: y = a(x - h)^2 + k
Theorems
Vertex form of a parabola
Properties of parabolas
Suitable Grade Level
Grades 8-10