Math Problem Statement

The graph of a function is given below. Give all x-intercepts and y-intercepts shown.

Solution

From the graph provided:

  1. X-intercepts: These are the points where the graph intersects the x-axis. At these points, y=0y = 0. The x-intercepts are approximately: (2,0)and(2,0)(-2, 0) \quad \text{and} \quad (2, 0)

  2. Y-intercept: This is the point where the graph intersects the y-axis. At this point, x=0x = 0. The y-intercept is: (0,2)(0, -2)

Summary:

  • X-intercepts: (2,0)(-2, 0) and (2,0)(2, 0)
  • Y-intercept: (0,2)(0, -2)

Would you like me to explain how to find these points or discuss more about intercepts?


Related Questions:

  1. How do you determine the x-intercepts and y-intercepts algebraically from a quadratic equation?
  2. Can a graph have more than two x-intercepts? Explain.
  3. What is the significance of the vertex of this parabola?
  4. How do we write the equation of a parabola given the x-intercepts and y-intercept?
  5. What transformations can shift this parabola horizontally or vertically?

Tip: The x-intercepts are also called the roots or zeros of the function because they satisfy f(x)=0f(x) = 0.

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Math Problem Analysis

Mathematical Concepts

Intercepts of a function
Parabolas
Graph reading

Formulas

X-intercept: y = 0
Y-intercept: x = 0

Theorems

Intercepts occur where the graph crosses the axes

Suitable Grade Level

Grades 8-10