Math Problem Statement
A quadratic function y, equals, f, of, xy=f(x) is plotted on a graph and the vertex of the resulting parabola is left parenthesis, minus, 4, comma, 5, right parenthesis(−4,5). What is the vertex of the function defined as g, of, x, equals, f, of, minus, x, minus, 3g(x)=f(−x)−3?
Solution
To find the vertex of the function , we start with the vertex of , which is at .
- The transformation reflects the graph across the y-axis. Thus, the vertex of becomes .
- The transformation shifts the graph downward by 3 units. This moves the vertex from to .
Therefore, the vertex of is .
Would you like more details or do you have any questions? Here are some related questions for further exploration:
- How does the reflection across the y-axis affect the function's graph?
- What are the general effects of shifting a function vertically or horizontally?
- How can you derive the standard form of a quadratic function from its vertex?
- What are some real-life applications of quadratic functions?
- Can you explain the significance of the vertex in the context of a quadratic function?
Tip: Always note the transformations applied to functions, as they significantly impact the graph's features!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Transformations
Formulas
Vertex form of a quadratic function
Transformations of functions
Theorems
Vertex transformation for quadratic functions
Suitable Grade Level
Grades 8-10