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.

Would you like more details or have any questions?

Here are some related questions to explore:

  1. What is the effect of a horizontal shift on the vertex of a parabola?
  2. How does a vertical stretch or compression affect the vertex?
  3. How does adding a constant to a quadratic equation affect the graph?
  4. Can a reflection over the x-axis or y-axis change the vertex position?
  5. How do you find the vertex of a parabola given its equation?

Tip: The formula for the vertex of a quadratic equation y=ax2+bx+cy = ax^2 + bx + c is (b2a,f(b2a))\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right), 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