Math  /  Algebra

QuestionGraph the function f(x)=(x+5)24f(x)=(x+5)^{2}-4 by starting with the graph of y=x2y=x^{2} and using transformations (shifting, stretching/compressing, and/or reflecting).
Use the graphing tool to graph the function.
Click to enlarge graph

Studdy Solution
Start with the graph of y=x2 y = x^2 .
Apply the horizontal shift: Move the graph 5 units to the left to obtain y=(x+5)2 y = (x+5)^2 .
Apply the vertical shift: Move the graph 4 units downward to obtain y=(x+5)24 y = (x+5)^2 - 4 .
The vertex of the parabola is now at (5,4) (-5, -4) .
The graph of the function f(x)=(x+5)24 f(x) = (x+5)^2 - 4 is a parabola with its vertex at (5,4) (-5, -4) , opening upwards.

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