標題:
F.4 Functions and Graphs
Find the optimum values of the following functionsS 1. y = 2x^2 +10x + 5 2. y = -3x^2 + 9x - 2 P.S: I want to know how to do and i still want to know optimum value is it the same as max.value or mini. values, thanks
最佳解答:
y = ax2 + bx + c y = a[x2 + (b/a)x] + c y = a[x2 + 2(b/2a)x] + c y = a[x2 + 2(b/2a)x + (b/2a)2 - (b/2a)2] + c y = a[x2 + 2(b/2a)x + (b/2a)2] - a(b/2a)2 + c y = a[x2 + 2(b/2a)x + (b/2a)2] - ab2/(4a2) + c y = a(x + b/2a)2 - b2/(4a) + c y = a(x + b/2a)2 - (b2-4ac)/(4a) 1. y = 2x2 +10x + 5 = 2(x2 +5x) + 5 = 2(x2 +5x+2.52 - 2.52) + 5 = 2(x2 +5x+2.52) - 2*2.52 + 5 = 2(x + 2.5)2 - 7.5 min y = -7.5 (this is the optimum value) corresponding value of x = -2.5 2. y = -3x2 + 9x - 2 = -3(x2 - 3x) - 2 = -3(x2 - 3x + 1.52 - 1.52) - 2 = -3(x2 - 3x + 1.52) + 3*1.52 - 2 = -3(x - 1.5)2 + 4.75 max y = 4.75 (this is the optimum value) corresponding value of x = 1.5 Method: Completing squares Optimum value = Maximum value or minimum value
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F.4 Functions and Graphs
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發問:Find the optimum values of the following functionsS 1. y = 2x^2 +10x + 5 2. y = -3x^2 + 9x - 2 P.S: I want to know how to do and i still want to know optimum value is it the same as max.value or mini. values, thanks
最佳解答:
y = ax2 + bx + c y = a[x2 + (b/a)x] + c y = a[x2 + 2(b/2a)x] + c y = a[x2 + 2(b/2a)x + (b/2a)2 - (b/2a)2] + c y = a[x2 + 2(b/2a)x + (b/2a)2] - a(b/2a)2 + c y = a[x2 + 2(b/2a)x + (b/2a)2] - ab2/(4a2) + c y = a(x + b/2a)2 - b2/(4a) + c y = a(x + b/2a)2 - (b2-4ac)/(4a) 1. y = 2x2 +10x + 5 = 2(x2 +5x) + 5 = 2(x2 +5x+2.52 - 2.52) + 5 = 2(x2 +5x+2.52) - 2*2.52 + 5 = 2(x + 2.5)2 - 7.5 min y = -7.5 (this is the optimum value) corresponding value of x = -2.5 2. y = -3x2 + 9x - 2 = -3(x2 - 3x) - 2 = -3(x2 - 3x + 1.52 - 1.52) - 2 = -3(x2 - 3x + 1.52) + 3*1.52 - 2 = -3(x - 1.5)2 + 4.75 max y = 4.75 (this is the optimum value) corresponding value of x = 1.5 Method: Completing squares Optimum value = Maximum value or minimum value
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