Math Problem Statement
Graph the function f(x) = (1/2 x squared and tell the the domain,range,X and y intercep,
Solution
Here is the graph of . As you can see, the parabola opens upwards, and both the x-intercept and y-intercept occur at the origin . The vertex at represents the minimum point of the function.
Summary:
- Domain:
- Range:
- X-intercept:
- Y-intercept:
Would you like more details or have any further questions?
Related Questions:
- What is the effect of changing the coefficient in front of on the graph of a parabola?
- How would the graph of differ from this one?
- Can you explain how to find the vertex of a parabola in the general form ?
- What happens to the domain and range if the equation is shifted upwards by adding a constant?
- How do you determine the axis of symmetry for a quadratic function?
Tip:
When graphing quadratic functions, the coefficient of determines the "width" and direction of the parabola. A smaller coefficient makes the parabola wider, while a larger one makes it narrower.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Graphing
Formulas
f(x) = (1/2)x^2
Theorems
Properties of Quadratic Functions
Suitable Grade Level
Grades 8-10
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