Standard form to Vertex Calculator

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Standard form of Quadratic equation is written as ax2 + bx + c, where a, b and c are coefficients and x and y are variables. The vertex form of parabola or quadratic equation is written as y = m(x-h)2 + k. To convert standard form to vertex form is done in 5 steps. 


Example 1: Convert this parabola equation from standard to vertex form
2x2 -28x+10.

Step 1 : 2x2 – 28x + 10= 2(x2 – 14x) + 10  (1st two terms are factorized)

Step 2: -14/2= -7 , 7x7= 49 (coefficient of x term 14/2 and then squared)

Step 3: 2(x2 – 14x + 49) + 10 - (49x2) (49 is added inside and its double is subtracted)

Step 4:  2(x2 – 14x + 49) + 10 – 98 (Simplification)

Step 5: 2 (x-7)2 – 88 (Parentheses converted to squared unit)



Example 2: Convert this parabola equation from standard to vertex form
2x2 +12x - 4.

Step 1 : 2x2 + 12x – 4= 2(x2+ 6x)- 4 (1st two terms are factorized)

Step 2:  6/2= 3, 3x3= 9 (coefficient of x term 6/2 and then squared)

Step 3: 2(x2 + 6x + 9) - 4 - (9x2) (9 is added inside and its double is subtracted)

Step 4:  2(x2 + 6x + 9)- 4- 18 (Simplification)

Step 5: 2 (x-3)2-22 (Parentheses converted to squared unit)

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