Outcome: C22, Solve Quadratic Equations
Originators: Daniel and Alex
Explaination: To find x intercepts using factoring you must first set y=0. If you are looking for a x at a certain point you must first set y = to that number. This is true for every way you can solve. and then break the right side of the equation down into 2 brackets. You know that one or both is equal to 0 because the answer is 0. Set it up so both individual brackets are equal to 0 and solve for x. You should two answers.(they may be the same). To solve using completing the square you must subract the c value from both sides and then factor out the a value from the right side. Now take b and divide it by 2 and then square it. Add this number to both sides. Be careful to mutiply it by "a" before you add it to the left if you have factored out an a coefficent. Now divide both sides by "a" and take the square root of both sides. The left side should be a positive AND a negative. If you took the square root of a negative it the solution will be imaginary. Now solve for x when it is positive and when its negative. You should have 2 solutions(they may be the same). To solve using the quadratic formula you must put your equation into general form so that a,b and c can be seen cleary. Now enter them into the quadratic formula. Do all work under the square root sign first and factor out perfect squares if needed. Now solve for when the sign before the square root is positive, and then when it is negative. You will have 2 solutions (again they may be the same). If the number under the square root was a negative then the answer will be imaginary, if that is the case put it in complex form.
Sample Problem: solve for x (roots, x intercept) for the equation.
y = 2x² 5x + 257.125
Solution: The example below is using the quadratic formula method.
0 = 2x² 5x + 257.125

(5)±√((5)²(4*(2)(257.125)))
x= 2*(2)

5 ±√(25  2057 )
x = 4

5 ± √(2032)
x = 4 4

5 ± √(16* 127)
x = 4 4

5 ± 4*√(127)
x = 4 4

x = 1.25 ±√(127)

In this case the answer is complex, which means the equation has no x intercepts or roots.
Comments (1)
Anonymous said
at 8:11 pm on Mar 13, 2007
Dan and Alex, nice work.
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