Math Problem Statement
Solution
Here is a solution based on the given graph of the parabola:
(a) Does the parabola open upward or downward?
The parabola opens downward, as it has a maximum point (vertex) and the arms point downward.
(b) Find the coordinates of the vertex.
From the graph, the vertex is located at the highest point of the parabola: Vertex: (2, 4).
(c) Find the equation of the axis of symmetry.
The axis of symmetry is a vertical line passing through the vertex. Since the vertex's x-coordinate is , the equation is: Axis of symmetry: .
(d) Find the intercept(s).
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x-intercepts: These are the points where the parabola crosses the x-axis. From the graph, these are approximately: x-intercepts: (0, 0) and (4, 0).
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y-intercept: This is the point where the parabola crosses the y-axis. From the graph, this is: y-intercept: (0, 0).
If you need further clarifications or have any additional questions, feel free to ask!
Here are five follow-up questions for deeper understanding:
- What is the general formula for the equation of a parabola in vertex form?
- How do you verify the vertex coordinates algebraically?
- What determines whether a parabola opens upward or downward in its equation?
- How can you calculate the intercepts using the quadratic formula?
- What role does the axis of symmetry play in analyzing a parabola?
Tip: Always double-check vertex and intercept values on graphs by substituting them into the equation of the parabola.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Parabolas
Vertex
Axis of Symmetry
Intercepts
Formulas
Equation of a parabola in standard form: y = ax^2 + bx + c
Axis of symmetry: x = -b/(2a)
Theorems
Properties of parabolas in the context of quadratic functions
Suitable Grade Level
Grades 8-10
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