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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 y=f(x+2)y = f\left(x+2\right) with f(x)=x2f\left(x\right) = {x}^{2}. The parent's lowest output comes when f receives 0. Here f receives x+2x+2, 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 x+2=2x+2 = 2 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. f(x+2)f\left(x+2\right) is zero inside at -2, and f(x−2)f\left(x-2\right) at 2.

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Challenge

Draw the graph of y=f(x+3)y = f\left(x+3\right) for f(x)=x2f\left(x\right) = {x}^{2}. The faint curve is f itself. Drag the vertex, then the second point.

Try it yourself

y=f(x+3)y = f\left(x+3\right)

Draw the parabola

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

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