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Question

How to change standard form to vertex form of a parabola?


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Solution

Step 1: Different forms of equations of parabola:

The standard form of a parabola is y=ax2+bx+c

Vertex form of parabola is y=a(x-h)2+k

(h,k) represents the vertex of the parabola.

If (a<0) then parabola has the maximum value at (h,k).

if a>0 then parabola has the minimum value at (h,k).

Step 2: Calculation of vertex form:

Compare the standard and vertex forms and use the below formulas to get the vertex form of a parabola.

h=-b2a,k=-D4a[D=b2-4ac]

Hence, we can find the vertex form of a parabola using the above method.


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