What is the vertex form of y=-3x^2 + 12x - 8y=−3x2+12x−8?

1 Answer
Pris
Dec 21, 2016

The vertex form of y=-3x^2+12x-8y=−3x2+12x−8 is y=-3(x-2)^2+4y=−3(x−2)2+4

Explanation:

To derive vertex form y=a(x-h)^2+ky=a(x−h)2+k from general quadratic form y=ax^2+bx+cy=ax2+bx+c,
you can use completing the square

y=-3x^2+12x-8y=−3x2+12x−8
= -3 (x^2-4x+8/3)=−3(x2−4x+83)
= -3 (x^2-4x +(-2)^2-(-2)^2 +8/3)=−3(x2−4x+(−2)2−(−2)2+83)
= -3 ((x-2)^2 -4+8/3)=−3((x−2)2−4+83)
= -3 ((x-2)^2 -4/3)=−3((x−2)2−43)
= -3 (x-2)^2 -4=−3(x−2)2−4

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