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Question

How to find the vertex of a parabola

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Solution

Dear Student,

Mention below is the derivation for finding the vertex of a parabola:
We have,y=ax2+bx+c=ax2+bax+ca=ax2+2×b2a×x+b2a2-b2a2+cay=ax+b2a2+4ac-b24a2y-4ac-b24a=ax+b2a2As, the standard form of the parabola is Y=4AX2, whose vertex is V0,0Y=y-4ac-b24a, X=x+b2a and A=a4So, the vertex of the given function is given by:X=0 and Y=0y=4ac-b24a, x=-b2aSo, the vertex of y=ax2+bx+c is V4ac-b24a,-b2a.
Regards

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