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Vertex form of a quadratic worksheets Grades 10–11

Complete the square to write y = a(x − h)² + k and name the vertex.

The front of the free vertex form of a quadratic worksheet
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How to do it

Complete the square to write y = a(x − h)² + k. The vertex is (h, k).

y=x2+2x−6→y=(x+1)2−7y = x^{2} + 2x - 6\quad \to \quad y = (x + 1)^{2} - 7
y=(x2+2x+1)−7y = (x^{2} + 2x + 1) - 7add (2 ÷ 2)² = 1 inside and subtract it outside
y=(x+1)2−7y = (x + 1)^{2} - 7write the square; the vertex is (−1, −7)

Example problems

  1. y=−x2−2x+10→y = -x^{2} - 2x + 10\quad \to \quad
  2. y=x2+8x+13→y = x^{2} + 8x + 13\quad \to \quad
  3. y=x2+10x+35→y = x^{2} + 10x + 35\quad \to \quad
  4. y=x2+14x+55→y = x^{2} + 14x + 55\quad \to \quad

Quadratic and polynomial functions

  1. Vertex form of a quadratic
  2. Finding the vertex from standard form
  3. The discriminant
  4. Quadratic equations with complex roots
  5. Polynomial long division
  6. Synthetic division
  7. The remainder theorem
  8. The factor theorem
  9. The rational root theorem