Math Problem Statement

Which equation represents the relationship between x and y in the table? The table values are: x = [0, 1, 3, 4, 6] and y = [0, 1, 9, 16, 36].

Solution

Let's analyze the table and find the correct equation that represents the relationship between xx and yy.

The values in the table are:

  • For x=0x = 0, y=0y = 0
  • For x=1x = 1, y=1y = 1
  • For x=3x = 3, y=9y = 9
  • For x=4x = 4, y=16y = 16
  • For x=6x = 6, y=36y = 36

It seems that the yy values are the squares of the corresponding xx values. Let's confirm that this follows the equation y=x2y = x^2:

  • y(0)=02=0y(0) = 0^2 = 0
  • y(1)=12=1y(1) = 1^2 = 1
  • y(3)=32=9y(3) = 3^2 = 9
  • y(4)=42=16y(4) = 4^2 = 16
  • y(6)=62=36y(6) = 6^2 = 36

This matches perfectly, so the correct equation is y=x2y = x^2.

Thus, the correct answer is A: y=x2y = x^2.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

  1. What happens if we try a different function, like a cubic function, on the same table of values?
  2. How would the graph of y=x2y = x^2 look compared to other quadratic functions like y=(x+1)2y = (x+1)^2?
  3. What are the characteristics of quadratic functions like y=x2y = x^2?
  4. Can we solve for xx given y=x2y = x^2 for larger values of yy?
  5. How does the transformation of functions affect the shape of the graph for quadratic equations?

Tip: When analyzing relationships in a table, always check if a simple polynomial (like x2x^2 or x3x^3) or other patterns (like linear) match the data points!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions

Formulas

y = x^2

Theorems

Properties of quadratic functions

Suitable Grade Level

Grades 7-9