SOLUTION: c)(i) Write the quadratic expression x^2-34x+9 in completed square form (ii) use the completed square form from part (c) (i) to solve the equation x^2-34x+9=0, leaving your answ

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Question 766811: c)(i) Write the quadratic expression x^2-34x+9 in completed square form
(ii) use the completed square form from part (c) (i) to solve the equation x^2-34x+9=0, leaving your answer in exact (surd) form
(iii) use the completed square form from part (c)(i)to write down the vertex of the parabola y=x^2-34x+9
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
c)(i) Write the quadratic expression in completed square form
Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form


Start with the given equation



Subtract from both sides



Factor out the leading coefficient



Take half of the x coefficient to get (ie ).


Now square to get (ie )





Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation




Now factor to get



Distribute



Multiply



Now add to both sides to isolate y



Combine like terms




Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation we get:


Graph of . Notice how the vertex is (,).



Notice if we graph the final equation we get:


Graph of . Notice how the vertex is also (,).



So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.





(ii) use the completed square form from part (c) (i) to solve the equation , leaving your answer in exact (surd) form

(iii) use the completed square form from part (c)(i)to write down the vertex of the parabola
....compare to and you will see that and which means
the vertex of the parabola is at (,

since the graph above is not good, I will make another one for you to see it is a parabola:




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