The Sign Inside
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 32 of 55.
A plus inside the brackets moves the graph left, which surprises most people at first. Take with . The parent's lowest output comes when f receives 0. Here f receives , and that is 0 when x is -2. So the vertex is at (-2, 0), two places left.
Follow one more point to see why. On the parent, input 2 gives 4: the point (2, 4). On the new graph, f must receive 2, so and x is 0. The point with height 4 is now (0, 4). The rule adds 2 to x before f sees it, so x has to be 2 smaller to feed f the same number, and smaller x means further left.
So do not guess from the sign. Ask where the inside of the brackets is 0: that is where the vertex goes. is zero inside at -2, and at 2.
Challenge
Draw the graph of for . The faint curve is f itself. Drag the vertex, then the second point.
Try it yourself
Draw the parabola
This lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Functions & Transformations
4Combining Functions
Adding FunctionsSubtracting FunctionsMultiplying FunctionsAt a Single NumberRecap: Combining10Functions in Stories
Writing the RuleUsing the RuleWorking BackwardUndoing a ConversionRecap: Stories5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip