Math Problem Statement
Solution
Let's analyze the graph and solve the problems based on the quadratic equation provided.
Step-by-step analysis of the graph:
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Identifying the vertex: From the graph, we can see the parabola opens upwards, and the vertex is the lowest point. The x-coordinate of the vertex is at (given), and the y-coordinate looks to be at . Therefore, the vertex is:
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Identifying the y-intercept: The y-intercept occurs where the parabola crosses the y-axis (i.e., where ). From the graph, this happens at .
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Identifying the x-intercepts: The x-intercepts occur where the parabola crosses the x-axis (i.e., where ). From the graph, the x-intercepts appear to be at and , so the intercepts are:
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Equation of the axis of symmetry: The axis of symmetry for a parabola passes through the vertex and is a vertical line. Since the x-coordinate of the vertex is , the equation of the axis of symmetry is:
Summary:
- Vertex:
- Y-intercept:
- X-intercepts: and
- Axis of symmetry:
Would you like more details or have any questions on any part?
Related questions:
- How do you determine the vertex of a parabola algebraically?
- How can you derive the quadratic equation from the vertex and intercepts?
- What is the significance of the axis of symmetry in a quadratic function?
- How do you calculate the y-intercept of a parabola from its equation?
- What are the steps to find the x-intercepts using the quadratic formula?
Tip: For a quadratic equation in vertex form, , the vertex is , and the axis of symmetry is .
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Graphing Parabolas
Vertex and Intercepts
Formulas
Vertex form: y = a(x - h)^2 + k
Standard form: y = ax^2 + bx + c
Theorems
Parabola Symmetry
Zeroes of a Quadratic Function
Suitable Grade Level
Grades 9-11
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