Math Problem Statement
Solution
To find the quadratic function that represents the given graph, let’s analyze the provided information.
Step-by-Step Solution:
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Vertex Form of a Quadratic Function: The vertex form of a quadratic function is given by:
where:
- is the vertex of the parabola.
- determines the shape and direction (upward or downward) of the parabola.
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Identify the Vertex: From the graph, the vertex is clearly labeled as . So, and .
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Substitute the Vertex into the Equation: The equation in vertex form becomes:
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Find the Value of : To find , use another point on the graph. From the graph, a clear point is .
Plugging in and :
Simplifying:
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Final Equation: The equation of the quadratic function is:
This is the quadratic function that represents the given graph.
Would you like more details or have any questions? Here are some related questions to deepen your understanding:
- How would the graph change if were negative?
- What is the significance of the vertex in a quadratic function?
- How do we convert from the vertex form to the standard form of a quadratic equation?
- What other points on the graph can we use to verify ?
- How does changing or affect the position of the parabola?
Tip: Always use a clear point on the graph, preferably an intercept, to solve for accurately.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Formulas
Vertex form of a quadratic function: f(x) = a(x - h)^2 + k
Theorems
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Suitable Grade Level
Grades 9-12