The graph below shows a blue and red parabola. The blue parabola represents a quadratic written in the vertex form [math]f\left(x\right)=a\left(x-h\right)^2+k[/math] where [i]a[/i] represents the dilation, [i]h[/i] represents the horizontal shift, and[i] k[/i] represents the vertical shift. The red parabola is its inverse. [br][br]Move the sliders around and answer the following questions:
1. When does the blue graph have two unique solutions?
2. When does it have a single solution?
3. When does it have complex solutions?
In the TI Nspire activity, we explored roots using the quadratic formula. Let's explore the same concept but with complex roots. Does the same reasoning apply? Play around with the graph below and find out!
To get started try the equation [math]f\left(x\right)=2x^2-8x+10[/math]. What is the x value of its vertex and the distances from this x value? What are its roots using the TI way of thinking? Check your answer by using the quadratic formula.