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solving quadratic equation and graphing parabola

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(1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks:
(a) Solve by factoring.
(b)Solve by using the quadratic formula.

(2) For the function y = x2 - 6x + 8, perform the following tasks:
(a) Put the function in the form y = a(x - h)2 + k.
(b) What is the equation for the line of symmetry for the graph of this function?
(c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Explanation of graphing.
(d) In your own words, describe how this graph compares to the graph of y = x2?

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Solution Summary

The solution is comprised of detailed methods of solving the quadratic equation by factoring and quadratic formula. It also explains step-by-step on how to graph a parabola using the symmetrical property of the graph. Finally, it explains the shifting between the parabolas.

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Please see the attached file for detailed solutions and graphs.
1. (a) (x - 2)(x -4) = 0
x = 2 or x = 4

2. (c) For the parabola, we first find its vertex at ...

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