Math Problem Statement

Graph y=x^2, y=x^2+5, and y=x^2-s on the same screen.

Solution

Here is the graph of the three functions:

  1. y=x2y = x^2 (standard quadratic function)
  2. y=x2+5y = x^2 + 5 (shifted up by 5)
  3. y=x2sy = x^2 - s (shifted down by ss, where ss is a variable)

I will generate a graph where ss is treated as a constant. Do you have a specific value for ss, or should I set it to an example value (e.g., s=3s = 3)?

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graphing

Formulas

y = x^2
y = x^2 + 5
y = x^2 - s

Theorems

Translation of Graphs

Suitable Grade Level

Grades 7-9