Math Problem Statement
f(x)=−x2+6x−10f(x)=-x2+6x-10 Write the Vertex as an Ordered Pair
Solution
To find the vertex of the quadratic function , we can use the vertex formula. For a function in the form , the x-coordinate of the vertex is given by:
In this case:
- Calculate the x-coordinate of the vertex:
- Substitute back into the function to find the y-coordinate of the vertex:
Thus, the vertex of the function is:
The vertex as an ordered pair is .
Would you like a breakdown of the steps or have any questions?
Here are five related questions for further practice:
- How would you find the vertex of ?
- What is the effect of the coefficient on the orientation of the parabola?
- How can you determine if the vertex is a maximum or minimum point?
- How would the vertex formula apply if ?
- How does changing the constant term affect the vertex?
Tip: For any quadratic function, the vertex can be thought of as the "turning point" of the parabola.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex Form
Formulas
Vertex formula: x = -b / 2a
Quadratic function: f(x) = ax^2 + bx + c
Theorems
Vertex theorem for parabolas
Suitable Grade Level
Grades 8-10
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