Math Problem Statement
Solution
The graph represents a parabola, and the equation given is , with the range of the parabola being . The vertex is at the point , and one of the points on the parabola is .
We are tasked with finding the value of .
Step-by-step approach:
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Vertex form of the parabola: Since the vertex is given at , we can start by writing the equation in vertex form: where . This gives us:
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Using the point : Now, substitute and into the equation to find : Simplify the equation: Solve for :
Thus, the value of is .
Answer: The correct option is A) .
Would you like a more detailed explanation or help with another question?
Here are some related questions:
- How do you find the vertex of a parabola from its equation in standard form?
- What is the significance of the value of in a parabola's equation?
- How do you convert from vertex form to standard form for a parabola equation?
- What does the range of a parabola tell you about its graph?
- How do you determine the direction a parabola opens based on its equation?
Tip: Always double-check the vertex and points on the graph to ensure accuracy in solving for the constants in the equation.
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Vertex Form of a Parabola
Coordinate Geometry
Formulas
Vertex form of a parabola: y = a(x - h)^2 + k
Theorems
The vertex form of a parabola represents its minimum or maximum point.
Suitable Grade Level
Grades 9-11