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David Davis
Mathematics
9 September, 18:44
Express x^2-5x+8 in the form (x-a) ^2+b
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Trevon Dougherty
9 September, 18:59
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x^2 - 5x + 8 = (x - 5/2) ^2 + 7/4
Step-by-step explanation:
(x - a) ^2 + b = x^2 - 2ax + a^2 + b
equate to your quadratic:
x^2 - 5x + 8 = x^2 - 2ax + (a^2 + b)
equating coefficients (ignoring x^2 as the coefficient is 1 for both)
for x:
-5 = - 2a - -> a = 5/2
for x^ (0) : 8 = a^2 + b, note a = 5/2
thus,
8 = (5/2) ^2 + b
8 = 25/4 + b
b = 8 - 25/4 = 32/4 - 25/4 = (32 - 25) / 4 = 7/4
hence a = 5/2, b = 7/4
thus,
x^2 - 5x + 8 = (x - 5/2) ^2 + 7/4
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