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 f(x)=12x2f(x) = \frac{1}{2}x^2. As you can see, the parabola opens upwards, and both the x-intercept and y-intercept occur at the origin (0,0)(0,0). The vertex at (0,0)(0,0) represents the minimum point of the function.

Summary:

  1. Domain: (,)(-\infty, \infty)
  2. Range: [0,)[0, \infty)
  3. X-intercept: (0,0)(0, 0)
  4. Y-intercept: (0,0)(0, 0)

Would you like more details or have any further questions?

Related Questions:

  1. What is the effect of changing the coefficient in front of x2x^2 on the graph of a parabola?
  2. How would the graph of f(x)=12x2f(x) = -\frac{1}{2}x^2 differ from this one?
  3. Can you explain how to find the vertex of a parabola in the general form ax2+bx+cax^2 + bx + c?
  4. What happens to the domain and range if the equation is shifted upwards by adding a constant?
  5. How do you determine the axis of symmetry for a quadratic function?

Tip:

When graphing quadratic functions, the coefficient of x2x^2 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