1. Graphing f(x) = ax^15
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The quadratic parent function is y=x^2. It can be transformed by multiplying by a factor a, obtaining the offspring function y=ax^2. How does this affect the graph of the original function?
See solution.
Notice that this function opens up. Nevertheless, this function can be transformed by multiplying by a factor a, obtaining the offspring function y=ax^2. If a<0 the function gets reflected in the x-axis, causing it to open downwards. If a>0 the function opens up, just as the parent function.
Notice that the parameter a on the graph of y=ax^2 can also cause a vertical stretch or vertical shrink.