Math Problem Statement
Solution
We are given the graph of (solid black curve) and asked to identify which function corresponds to the dotted orange curve from the provided options.
Observing the Dotted Graph:
- The dotted graph represents a parabola that is similar to , but it has been shifted horizontally and vertically.
- The vertex of the dotted graph appears to be at , whereas the vertex of is at the origin .
Applying the Vertex Form of a Parabola:
The general form for a parabola is:
where:
- is the vertex of the parabola,
- determines the direction and width of the parabola.
In this case, the dotted parabola seems to be shifted horizontally by (i.e., ) and vertically by (i.e., ).
Thus, the equation of the dotted parabola is:
Answer:
The correct function representing the dotted graph is .
Let me know if you'd like further details! Here are five related questions for practice:
- How would the equation change if the vertex were at ?
- What is the effect of the coefficient on the width of the parabola?
- How would you graph ?
- What is the vertex of the parabola ?
- How does shifting a parabola horizontally and vertically affect its equation?
Tip: The signs in and directly tell you the horizontal and vertical shifts.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Transformations
Formulas
y = a(x - h)^2 + k
Theorems
Vertex Form of a Parabola
Suitable Grade Level
Grades 9-10
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