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Properties of parabolas


Compare the graphs of quadratic functions in the form: y = ax2 + bx + c .

a. What are the coordinates of the y-intercept?
b. What must be true in order for the graph to reflect over the y-axis?
c. What must be true in order for the graph to open down? to open up?

 

 Extensions

d. What must be true in order for the graph to touch the x-axis only one time? zero times?
e. How can you calculate the equation of the axis of symmetry (the vertical line where the graph can be folded in half)?
f. Where on the graph is the solution for ax2 + bx + c = 0 ?



 Related External Resources

Exploring Parabolas [ java applet ]
This java demonstration shows a geometric construction of a parabola.



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