Answer to Question #163834 in Algebra for Vakel

Question #163834

5. The coordinates of the vertex of the curve y = 1 - 2x - 4x2 are:


6. If 2x2 - 12x + 11 ≡ 2(x + b)2 + c, then

                A. b = 6, c = -7               B. b = 3, c = -7          C. b = -3, c = -7               D. b = 3, c = 7


1
Expert's answer
2021-02-24T06:42:12-0500

Ans 5:-

Given curve is-

y=12x4x2y=1-2x-4x^2


y=14(x2+x214)y=\dfrac{-1}{4}(x^2+\dfrac{x}{2}-\dfrac{1}{4})


y=14(x2+x2+11611614)y=-\dfrac{1}{4}(x^2+\dfrac{x}{2}+\dfrac{1}{16}-\dfrac{1}{16}-\dfrac{1}{4})



y=14(x+14)2+564y=-\dfrac{1}{4}(x+\dfrac{1}{4})^2+\dfrac{5}{64}


On Comparing the above equation with y=a(xh)2+ky=a(x-h)^2+k


We get h=14,k=564h=\dfrac{-1}{4},k=\dfrac{5}{64}


We get the vertex as (14,564)(-\dfrac{1}{4},\dfrac{5}{64})


Ans 6:-

Given, 2x212x+11=2(x+b)2+c2x^2 - 12x + 11 = 2(x + b)^2 + c


2x212x+11=2(x2+b2+2xb)+c2x212x+11=2x2+2b2+4xb+c2x^2-12x+11=2(x^2+b^2+2xb)+c\\2x^2-12x+11=2x^2+2b^2+4xb+c


On comparing coefficient of Both the sides

we get 4b=12,2b2+c=114b=-12,2b^2+c=11


b=124=3b=\dfrac{-12}{4}=-3


2b2+c=11c=112(3)2c=112(9)c=1118=7\Rightarrow 2b^2+c=11\\\Rightarrow c=11-2(-3)^2\\\Rightarrow c=11-2(9)\\\Rightarrow c=11-18=-7


Hence The value of b=3 and c=7.b=-3 \text{ and } c=-7.



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