17maopao.com Free · No sign-up · Runs in your browser

Personal documents / Standard form to vertex form

Standard form to vertex form calculator

In short: turn y = ax² + bx + c into vertex form y = a(x − h)² + k, with the vertex and the steps.

Type the three coefficients from y = ax² + bx + c and get y = a(x − h)² + k — with the vertex, the axis of symmetry and the algebra written out.

Example: a = 2, b = −8, c = 5 gives y = 2(x − 2)² − 3.

Vertex form

y = 2(x − 2)² − 3

      How the conversion works

      Step 1. Find h = −b ÷ (2a): the x-coordinate of the vertex.
      Step 2. Find k = c − b² ÷ (4a): the y-coordinate, which is the value of the function at x = h.
      Step 3. Write y = a(x − h)² + k, keeping the same a.

      What it does not do

      It does not draw the parabola and it does not solve equations. It converts the form and reports the vertex, the axis of symmetry, the discriminant and the real roots; those are enough to sketch the curve by hand.

      Questions

      What is vertex form?

      Vertex form is y = a(x − h)² + k, where (h, k) is the vertex and x = h is the axis of symmetry.

      How do I find h and k?

      h = −b ÷ (2a) and k = c − b² ÷ (4a); the steps above show the substitutions with your numbers.

      What if a is negative?

      The maths is the same — a negative a just opens the parabola downward.

      Why can a not be zero?

      If a = 0 there is no x² term and you have a straight line, not a parabola.

      Is the answer exact?

      Six decimal places, plus exact fractions when a, b and c are whole numbers.

      Is my input uploaded?

      No; everything is calculated in your browser.