Math Problem Statement
Solution
The function provided is , and you are asked to find the vertex.
This function is in vertex form, which is , where:
- is the vertex.
- determines the width and direction of the parabola.
From the equation :
- The term shows that (since can be written as ).
- The constant represents , so .
Therefore, the vertex is .
The correct answer is .
Would you like any further details or clarifications?
Here are 5 follow-up questions related to this topic:
- How does the value of affect the shape of the parabola?
- Can you find the axis of symmetry for this quadratic function?
- What happens to the vertex if we change the equation to ?
- How do you find the x-intercepts of this quadratic function?
- What is the y-intercept of the given quadratic function?
Tip: The vertex form of a quadratic function directly reveals the vertex, making it easy to identify key properties like the maximum or minimum point!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex Form
Formulas
Vertex form of a quadratic function: g(x) = a(x - h)^2 + k
Theorems
The Vertex Theorem for Quadratic Functions
Suitable Grade Level
Grades 9-11
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