How this calculation works
The constant term in standard form is the value at x=0. It differs from the vertex height unless the horizontal shift is zero.
THE FORMULA
a(x−h)²+k = ax²−2ahx+ah²+kA worked example
2(x−3)²−1 expands to 2x²−12x+17.
Good to know
For a parabola, the scale must be nonzero.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Expand a quadratic from vertex form and report its three standard coefficients.
The primary result is labeled “Coefficient of x²”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
For a parabola, the scale 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?
2(x−3)²−1 expands to 2x²−12x+17.
Which rule does this calculator apply?
a(x−h)²+k = ax²−2ahx+ah²+k