Math Problem Statement
true or false. A vertical shift would affect the x-value of the vertex.
Solution
False.
A vertical shift affects only the y-value of the vertex, not the x-value. The vertex of a parabola or any graph shifts up or down based on the vertical shift, but the x-coordinate remains unchanged.
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Here are some related questions to explore:
- What is the effect of a horizontal shift on the vertex of a parabola?
- How does a vertical stretch or compression affect the vertex?
- How does adding a constant to a quadratic equation affect the graph?
- Can a reflection over the x-axis or y-axis change the vertex position?
- How do you find the vertex of a parabola given its equation?
Tip: The formula for the vertex of a quadratic equation is , where the x-value depends on the coefficients of the quadratic, and the y-value depends on vertical shifts.
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Math Problem Analysis
Mathematical Concepts
Algebra
Graph Transformations
Quadratic Equations
Formulas
Vertex formula for quadratic equations: \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \)
Equation of a vertically shifted parabola: \( y = a(x - h)^2 + k \)
Theorems
Vertical shifts affect the y-value of the vertex only, while the x-value remains unchanged.
Suitable Grade Level
Grades 9-11
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