Graphs of Quadratic Functions
We will be looking at the affects of coefficients on the basic quadratic function. The blue function is the graph of f(x)=x^2. The green is the graph of the transformed function f(x)=a*(x+b)^2 + c where a, b, and c are the variables that can be changed.
1) What is the vertex and axis of symmetry for the original function? for the transformed function? 2) Use the sliders to get the transformed function graph to match up perfectly with the original function. What values of a, b, and c do you need? 3) What do you think the affect a has on the graph of a quadratic function? Try changing it and see what happens! 4) Repeat step 3 for b and c. 5) Use the sliders to make the quadratic graph have a vertex of (-6,2) where this graph opens down. What values of a, b, and c did you choose?