Let's tackle each transformation one step at a time. We begin by talking about whether the function will open up or down. We know that the sign of the coefficient a determines if the function will open up or down.
Consider the function f(x) = ax\(\small\mathsf{ ^2 }\).
Take a look at the two graphs below. What can you say about the a-value from the function for each graph shown? Click on the graph to see the correct answer.
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| If a is negative, then the graph is reflected over the x-axis and opens down. To the right is the graph of f(x) = -x\(\small\mathsf{ ^2 }\). | If a is positive, then the graph opens upwards. To the right is the graph of f(x) = x\(\small\mathsf{ ^2 }\). |
This reflection over the x-axis is the exact mirror image of the function that is not reflected. That is why we call this transformation a reflection.
