[size=150]The [b]Parent Square Root Function[/b] is [math]f\left(x\right)=\sqrt{x}[/math]. The [b]"kid" square root function is[/b] given by the equation, [math]f\left(x\right)=a\sqrt{bx-h}+k[/math]. With this activity, you will explore the values of [i]a, h, [/i]and [i]k[/i], and what effect these values have on the kid function![/size][br][br][size=150][color=#9900ff][b]YOU TRY: Set your [i]a [/i]slide bar to "1" and the other slide bars to "0." [/b][br][/color]What you see is the PARENT FUNCTION. Draw a sketch of this graph. Record the vertex, x-intercept, Domain & Range.[br][br][color=#9900ff]NOTE: [i]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.)[/i][br][br][b]YOU TRY: Use the slide bars to change the values of [/b][/color][b][i][color=#9900ff]a, h[/color], [/i][color=#9900ff]and [/color][i][color=#9900ff]k. Change them in multiple ways![br][/color][/i][/b][/size][size=150]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.[/size][br][br][size=150][color=#9900ff][i]1. What does the "a" do to the graph? Be specific. HINT! It can do THREE things.[br][/i]2. [i]What does the "h" do? Be specific.[br]3.[/i] [/color][i][color=#9900ff]What does the "k" do? Be specific.[br][/color][/i][/size][br][size=150]The [b]domain[/b] refers to the x-values that make-up our graph. [b]Ask yourself, "does the graph point to the left or right?" [/b] [br][br]Since the parent function starts at x = 0 and POINTS TO THE RIGHT, the [b]domain will be [/b][math]x\ge0[/math] or [[math]0,\infty[/math]). [size=100] *If the graph were to point LEFT, then the domain would be[/size] [math]x\le0[/math].[br][br]The [b]range[/b] refers to the y-values that make-up our graph. [b]Ask yourself, "is the curve CONCAVE or CONVEX?"[br][br][/b]Since the parent function is CONVEX and starts at y = 0, the range will be [math]y\ge0[/math][/size] or [[math]0,\infty[/math]).[br]*If the curve is CONCAVE, the range would be [math]y\le0.[/math][br][br][color=#9900ff][b][size=150]YOU TRY: How does manipulating the values of [i]a, h[/i] and [i]k[/i] affect the domain and range? [/size][/b][/color][br][br][size=150]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.[br][/size]