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Question

The coordinates of the vertex of a parabola represented by y=ax2+bx+c is, . Take D as discriminant;

A
(b2a,D4a)
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B
(b2a,D4a)
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C
(b2a,D4a)
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D
(b2a,D4a)
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Solution

The correct option is B (b2a,D4a)
We know that, the coordinates of the vertex of parabola of the form (xh)2=4a(yk) are (h,k)So, y=ax2+bx+c can be written as:ya=x2+bax+caya=x2+2b2ax+(b2a)2(b2a)2+caya=(x+b2a)2b24a2+ca(x+b2a)2=ya+b24a2ca(x+b2a)2=ya+D4a2(x+b2a)2=1a(y+D4a)Hence, the coordinates of the vertex of the given parabola is (b2a,D4a)

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