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# If the expression -0.5x^2+5x+20 is rewritten in the form of a(x-p)^2+q what is the value of q?

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If the expression -0.5x^2+5x+20 is rewritten in the form of a(x-p)^2+q what is the value of q?

Guest Feb 18, 2015

#2
+81004
+5

Here's another way to do this just by equating coefficients.....

a(x^2 - 2px  + p^2) + q  = -(1/2)x^2 + 5x + 20

ax^2 - 2apx + p^2 + q   =  -(1/2)x^2 + 5x + 20

Equating coefficients

a = -(1/2)

-2ap = 5 →   (-2)(-1/2)p  = 5 → p  = 5

And

ap^2 + q = 20

(-1/2)(5)^2 + q = 20  →   -25/2 + q = 20 →  q = 20 + 25/2  = 65/2 = 32.5 =  q

CPhill  Feb 18, 2015
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#1
+17711
+5

-0.5x2 + 5x + 20

Factor out the -0.5 from the first two terms:

-0.5(x2 - 10x) + 20

Complete the square:  divide -10 by 2 and square the answer:  (-10 ÷ 2)2 = 25

Add 25 inside the parantheses and add 12.5 at the end of the expression, so the value of the expression doesn't change (the reason that you add 12.5 is that you have entered -12.5 within the parantheses: -0.5 x 25 = -12.5):

-0.5(x2 - 10x + 25) + 20 + 12.5

-0.5(x - 5)2 + 32.5

Now, you can pick out p and q ...

geno3141  Feb 18, 2015
#2
+81004
+5

Here's another way to do this just by equating coefficients.....

a(x^2 - 2px  + p^2) + q  = -(1/2)x^2 + 5x + 20

ax^2 - 2apx + p^2 + q   =  -(1/2)x^2 + 5x + 20

Equating coefficients

a = -(1/2)

-2ap = 5 →   (-2)(-1/2)p  = 5 → p  = 5

And

ap^2 + q = 20

(-1/2)(5)^2 + q = 20  →   -25/2 + q = 20 →  q = 20 + 25/2  = 65/2 = 32.5 =  q

CPhill  Feb 18, 2015

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