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Worked solution

Reflect input coordinates in the y-axis

Use a graphing calculator to sketch (1) y=(x+1)(x−3)y=(x+1)(x-3) and (2) y=(−x+1)(−x−3)y=(-x+1)(-x-3). Copy the curves. What do you observe about the curves?

CJC · Transformations · Reflection in y-axis activity

Sketch and compare the coordinates

Answer

The minimum (1,−4)(1,-4) becomes (−1,−4)(-1,-4); the y-intercept stays (0,−3)(0,-3).

The Teacher completes the Student observation table. Both curves open upwards.

CurveMinimumy-interceptx-intercepts
(x+1)(x−3)(x+1)(x-3)(1,−4)(1,-4)(0,−3)(0,-3)(−1,0),(3,0)(-1,0),(3,0)
(−x+1)(−x−3)(-x+1)(-x-3)(−1,−4)(-1,-4)(0,−3)(0,-3)(1,0),(−3,0)(1,0),(-3,0)
Expand diagram

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Overlaid upward parabolas: original minimum (1,−4), roots −1 and 3; y-axis reflection minimum (−1,−4), roots 1 and −3. Both pass through (0,−3).
Overlaid upward parabolas: original minimum (1,−4), roots −1 and 3; y-axis reflection minimum (−1,−4), roots 1 and −3. Both pass through (0,−3).
Overlaid upward parabolas: original minimum (1,−4), roots −1 and 3; y-axis reflection minimum (−1,−4), roots 1 and −3. Both pass through (0,−3).
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Explain the reflection

Answer

y=f(−x)y=f(-x) reflects in the y-axis: (p,q)↦(−p,q)(p,q)\mapsto(-p,q).

Replace x by −x-x in y=f(x)y=f(x). The input coordinate changes sign while the output stays fixed. The source remark identifies this as signed scaling by −1-1 parallel to the x-axis. Points on the y-axis stay fixed.

How did this part go?