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:
- (in blue): This is the standard parabola with the vertex at the origin .
- (in red, dashed): This graph is a vertical translation of , shifted 4 units upwards.
Would you like more details on the transformation, or do you have any questions?
Here are 5 related questions:
- What effect would shifting by 4 units downwards have on the graph?
- How would the graph change if we used instead of ?
- What is the vertex form of a quadratic function, and how does it relate to these transformations?
- How does the graph of compare to the ones shown?
- Can you describe the transformation required to obtain from ?
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