How this calculation works
Recover the scale and shifts needed to write a quadratic as a square plus a constant.
THE FORMULA
ax²+bx+c = a(x−h)²+k with h=−b/(2a) and k=c−b²/(4a)A worked example
2x²−12x+17 becomes 2(x−3)²−1.
Good to know
The leading coefficient must be nonzero.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Recover the scale and shifts needed to write a quadratic as a square plus a constant.
The primary result is labeled “Vertex shift h”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The leading coefficient must be nonzero.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
2x²−12x+17 becomes 2(x−3)²−1.
Which rule does this calculator apply?
ax²+bx+c = a(x−h)²+k with h=−b/(2a) and k=c−b²/(4a)