In this exploration, you are to determine what is the effect of the changing coefficients and constant of the quadratic functions to its graph. [br][br]Follow the instructions below and give response to all of the questions.
You are given a parent function of the quadratic function in the form of [math]y=ax^2[/math]. Change the value of [i]a[/i] by sliding the slider.
Look at to the value of [i]a[/i], when the graph is concave up or down?
[list][*]The graph concave up when a > 0[/*][*]The graph concave down when a < 0[/*][/list]
Look at to the value of [i]a[/i], when the graph is narrower or wider?
[list][*]The greater the value of [i]a, [/i]the wider the graph.[/*][*]The lower the value of [i]a[/i], the narrower the graph. [/*][/list]
In the following, you are given a graph of [math]y=ax^2+c[/math] for different values of c between -10 to +10. Change the value of c by moving the slider c and keep the value of slider [i]a[/i] unchanged.
Explain, what happen to the graph when you change the value of [i]c[/i].
The intersection of the graph and the y-axis changes.
In the following, you are given a graph of [math]y=ax^2+bx+c[/math] for different values of a, b, and c between -10 to +10. [br]Change the value of b by moving the slider b and keep the value of slider [i]a and c[/i] unchanged.
Describe the effect of changing the value of [i]b [/i]to the graph.
[list][*]The changes of the coefficient [i]b[/i] change the coordinate of the vertex of the graph. [br]The higher the value of [/*][*]The higher the value of [i]b[/i] moves the graph to the left side of the y-axis and the lower the value of [i]b[/i] moves the graph to the right side of the y-axis.[/*][/list]
Use your findings to describe the similarities and differences in the shape of the graphs of each pair of quadratic functions below.[br][br][br]
[table][tr][td]f(x)[/td][td]g(x)[/td][td]similarities [/td][td]differences [/td][/tr][tr][td][math]2x^2+x+1[/math][/td][td][math]8x^2+x+1[/math][/td][td][br][br][br][br][/td][td][/td][/tr][tr][td][math]3x^2-1[/math][/td][td][math]-3x^2-1[/math][/td][td][br][br][br][br][br][/td][td][/td][/tr][tr][td][math]x^2+3[/math][/td][td][math]x^2-1[/math][/td][td][br][br][br][br][br][br][/td][td][/td][/tr][tr][td][math]x^2+x-1[/math][/td][td][math]x^2-x+1[/math][/td][td][br][br][br][br][br][br][/td][td][/td][/tr][/table]