Creating bounds on graph that zoom in based on student's input

Questions
1

If I want students to input an equation to see if it graphs as a linear or quadratic function, how can I set the bounds so that if they get creative and go beyond a -10 to 10 boundary that the graph will zoom in for them?

2

bounds: makeBounds(a,b,c,d)

You can make variables that use whatever parameters you want to use for the bounds.

3

What kind of parameters would you recommend here? Like, if a student is inputting a quadratic equation [for example y = (x - 50)(x+22) or y = -0.01x^2 - 16x + 22], how would we get the bounds to zoom out so that the graph’s “key points” always show up? (i.e. the vertex, y-intercept, and x-intercepts, if applicable)?

4

Sounds complicated. I mean y-intercept is simple enough. Maybe just use a full-screen graph (only have a graph component), so they can zoom in and out freely.

5

I’m trying to do something similar to this question so that I don’t have to change the graph every time I make a new activity when graphing different relationships. How do you define a,b,c,d to be the maximum and minimum values when those values can different each time?

6

You can have some sort of calculation done in the graph and then define variables in the CL pulling those values. In a quadratic, for example, you can calculate A, B, and C (of standard form) in the graph:

C=f(0)
B=f'(0)
A=f''(0)/2

Then use the quadratic formula for x-intercepts if present. You could also calculate h and k for the vertex. Add or subtract some units to make max and min values for x- and y-axes. Whatever you name those you can call them into the CL to use for bounds:

xmax=this.number(`x_{max}`)
xmin=this.number(`x_{min}`)
...etc
bounds: makeBounds(xmin, xmax, ymin, ymax)

You may have to get creative with calculations depending on your expectations of what student input may be.

7

Thank you for the reply!