GeoGebra Exploration: The Square Root Function
The Parent Square Root Function is . The "kid" square root function is given by the equation, . With this activity, you will explore the values of a, h, and k, and what effect these values have on the kid function!
YOU TRY: Set your a slide bar to "1" and the other slide bars to "0."
What you see is the PARENT FUNCTION. Draw a sketch of this graph. Record the vertex, x-intercept, Domain & Range.
NOTE: The square root function is the inverse of a quadratic function. Instead of an upright U-shape, it's a sideways-U (well, we're only looking at the "plus" or positive square root, so we only see one "side" of the "U" instead of the plus/minus which would show us both sides.)
YOU TRY: Use the slide bars to change the values of a, h, and k. Change them in multiple ways!
What do you notice? Record your observations onto a sheet of paper or create a Google doc with your notes. Pay particular attention to the questions below.
1. What does the "a" do to the graph? Be specific. HINT! It can do THREE things.
2. What does the "h" do? Be specific.
3. What does the "k" do? Be specific.
The domain refers to the x-values that make-up our graph. Ask yourself, "does the graph point to the left or right?"
Since the parent function starts at x = 0 and POINTS TO THE RIGHT, the domain will be or [). *If the graph were to point LEFT, then the domain would be .
The range refers to the y-values that make-up our graph. Ask yourself, "is the curve CONCAVE or CONVEX?"
Since the parent function is CONVEX and starts at y = 0, the range will be or [).
*If the curve is CONCAVE, the range would be
YOU TRY: How does manipulating the values of a, h and k affect the domain and range?
HINT! See below! There are essentially FOUR WAYS or DIRECTIONS the square root function can point in the coordinate plane. Determine the Domain and Range for each & record your answers.
