Math Problem Statement

Draw the graph of y=x^2 for the value of x from -4 to 4. Than using the transformation. Draw the graph of y=x^2+4.

Solution

Here are the graphs:

  1. y=x2y = x^2 (in blue): This is the standard parabola with the vertex at the origin (0,0)(0, 0).
  2. y=x2+4y = x^2 + 4 (in red, dashed): This graph is a vertical translation of y=x2y = x^2, shifted 4 units upwards.

Would you like more details on the transformation, or do you have any questions?


Here are 5 related questions:

  1. What effect would shifting y=x2y = x^2 by 4 units downwards have on the graph?
  2. How would the graph change if we used y=(x2)2y = (x - 2)^2 instead of y=x2y = x^2?
  3. What is the vertex form of a quadratic function, and how does it relate to these transformations?
  4. How does the graph of y=x2+4y = -x^2 + 4 compare to the ones shown?
  5. Can you describe the transformation required to obtain y=x23y = x^2 - 3 from y=x2y = x^2?

Tip: Vertical translations only affect the y-coordinates of the graph, moving it up or down without changing its shape.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing
Quadratic Functions
Transformations

Formulas

y = x^2
y = x^2 + 4

Theorems

Translation of Functions

Suitable Grade Level

Grades 8-10