Math Problem Statement
The graph of a function is given below. Give all x-intercepts and y-intercepts shown.
Solution
From the graph provided:
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X-intercepts: These are the points where the graph intersects the x-axis. At these points, . The x-intercepts are approximately:
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Y-intercept: This is the point where the graph intersects the y-axis. At this point, . The y-intercept is:
Summary:
- X-intercepts: and
- Y-intercept:
Would you like me to explain how to find these points or discuss more about intercepts?
Related Questions:
- How do you determine the x-intercepts and y-intercepts algebraically from a quadratic equation?
- Can a graph have more than two x-intercepts? Explain.
- What is the significance of the vertex of this parabola?
- How do we write the equation of a parabola given the x-intercepts and y-intercept?
- 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 .
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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