Quadratic Fathom Lab

The Ups and Downs of Quadratics

  1. Create 3 sliders by selecting slider from the Object menu and then new. A slider appears; it looks like a number line with a pointer on it. There is also some text that gives the name of the variables and its value, for example V1= 5. Change the name V1 to a. Create 2 more sliders and name them b and c.
  1. Create a function plot by selecting graph from the Object menu and then new. Click on the empty plot arrow and change the menu to function plot.
  1. Select plot function from the Graph menu. Type a*x^2+b*x +c. Click Apply and then OK. (You must press the right arrow after the ‘2’ and before the ‘+’ to move the curser from the exponent to the base line.)
  1. Now, move the sliders by graphing the sliders with the mouse. If you drag the number line, you can change the scale. Click on the arrow and see what happens.

Interactive Mathematics Program Year 3: Fireworks

The Ups and Downs of QuadraticsName______

Your task in this activity is to explore how the graph of a quadratic function is related to its coefficients. The specific questions here provide a framework for that exploration.

  1. If a quadratics function is written in the standard formy = ax2 + bx + c, where a, b, c are the coefficients, explain what happens to the graph when you change the leading coefficient a; what happens to the graph when you change the coefficient on the x ,b; what happens to the graph when you change the constant, c.

a –

b –

c –

  1. Explain how you can tell by looking at the coefficients of a quadratic function whether the vertex of the graph is a minimum or a maximum.

For Questions 2 through 4 begin by graphing the quadratic function defined by the equation

y=x2 + 5x + 3. Adjust the viewing window, so you get a good view of the graph.

  1. Try to create a new function whose graph is your original graph moved up or down. That is, the graph of the new function should have exactly the same shape as the original one, but the new vertex should be higher or lower on the screen. Describe your efforts and the results your get. Be sure to record the function you find and sketch its graph.
  1. Try to create a new function whose graph is your original graph moved left or right. That is, the graph of the new function should have exactly the same shape as the original one, but the new vertex should be to the left or right on the screen. Describe your efforts and the results your get. Be sure to record the function you find and sketch its graph.
  1. Try to create a new function that has the same vertex as your original graph but whose graph is “wider” or narrower”. Describe your efforts and the results you get, and record the function and its graph.

Interactive Mathematics Program Year 3: Fireworks