Math Problem Statement
Solution
To find the vertex of the quadratic function , we can use the vertex formula for a parabola given by . The x-coordinate of the vertex is calculated using:
For the given function :
Let's find the x-coordinate:
Now, substitute back into the function to find the y-coordinate:
So, the vertex of the function is at .
The correct answer is:
Would you like more details or have any questions? Here are some related questions:
- How do you derive the vertex formula ?
- What is the significance of the vertex in the graph of a parabola?
- How can you determine whether a parabola opens upward or downward?
- What role does the coefficient play in the shape of a quadratic function?
- How do you convert a quadratic function into vertex form?
Tip: The vertex form of a quadratic function, , makes it easier to identify the vertex, where is the vertex.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Parabolas
Formulas
Vertex formula: x = -b/(2a)
Standard form of a quadratic: f(x) = ax^2 + bx + c
Theorems
Properties of parabolas
Vertex of a parabola
Suitable Grade Level
Grades 9-12
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