SOLUTION: Rewrite the following equations in vertex form: Y=x^2-9x+20 Y=X^2-7x-8 Y=X^2+4x-9

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Rewrite the following equations in vertex form: Y=x^2-9x+20 Y=X^2-7x-8 Y=X^2+4x-9      Log On


   

Question 974252: Rewrite the following equations in vertex form:
Y=x^2-9x+20
Y=X^2-7x-8
Y=X^2+4x-9
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Y=x%5E2-9x%2B20
Y=%28x%5E2-9x%29%2B20......complete square
Y=%28x%5E2-9x%2Bb%5E2%29-b%5E2%2B20...compare to %28a-b%29%5E2=a%5E2-2ab%2Bb%5E2;as you can see, a=1 and 2ab=9
=>2%2A1%2Ab=9=>2b=9=>b=9%2F2, then we have
Y=%28x%5E2-9x%2B%289%2F2%29%5E2%29-%289%2F2%29%5E2%2B20
Y=%28x-9%2F2%29%5E2-81%2F4%2B20
Y=%28x-9%2F2%29%5E2-81%2F4%2B80%2F4
Y=%28x-9%2F2%29%5E2-1%2F4
=> h=9%2F2 and k=-1%2F4


Y=x%5E2-7x-8
Y=%28x%5E2-7x%29-8
Y=%28x%5E2-7x%2Bb%5E2%29-b%5E2-8...=>a=1 and2ab=7=>2%2A1%2Ab=7=>2b=7=>b=7%2F2, then we have
Y=%28x%5E2-7x%2B%287%2F2%29%5E2%29-%287%2F2%29%5E2-8
Y=%28x-7%2F2%29%5E2-49%2F4-8
Y=%28x-7%2F2%29%5E2-49%2F4-32%2F4
Y=%28x-7%2F2%29%5E2-81%2F4


Y=x%5E2%2B4x-9
Y=%28x%5E2%2B4x%29-9
Y=%28x%5E2%2B4x%2Bb%5E2%29-b%5E2-9...=>a=1 and2ab=4=>2%2A1%2Ab=4=>2b=4=>b=2, then we have
Y=%28x%5E2%2B4x%2B2%5E2%29-2%5E2-9
Y=%28x%2B2%29%5E2-4-9
Y=%28x%2B2%29%5E2-13


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite the following equations in vertex form:
Y=x^2-9x+20
x^2-9x = y-20
Complete the square to get:
x^2 - 9x + (9/2)^2 = y - (80/4) + (81/4)
(x-(4.5))^2 = y + (1/4)
===============================
Y=X^2-7x-8
x^2 - 7x = y+8
Complete the square to get:
x^2 - 7x + (7/2)^2 = y + (32/4) + (48/4)
(x-3.5)^2 = y+20
--------------------
Y=X^2+4x-9
I'll leave this to you.
Cheers,
Stan H.
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