X/y intercept for translations of f(x)

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The discussion focuses on how transformations of the function f(x) = x^2 + 2x + 2 affect its x-intercept, y-intercept, and vertex. Participants suggest converting the function into vertex form, f(x) = (x-h)^2 + k, to analyze changes more clearly. The transformation af(x) indicates a vertical stretch, impacting the y-values but not the x-intercept. The effects of other transformations like f(ax), -f(x), and f(-x) on intercepts and vertex are also explored. Understanding these transformations is essential for predicting how the graph will change based on the specific function.
roger
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Hello

please can you guys help me on this :

f(x) = x^2 + 2x + 2

af(x)=
f(ax)=
-f(x)=
f(-x)=


In each of the cases above, I wanted to know given a function, does the graph of it change in terms of the x intercept , y intercept and vertex ?

Does it depend on the particular function or not ?


Thanks in advance.

roger
 
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Why don't you first change that equation into transformation/vertex form
<br /> f(x) = (x-h)^2 + k<br />

The make up numbers for a and see how it changes.
 
af(x) represent the graph of f(x) is enlarged a times of the oringinal to the y-axis.
 
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