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Finding the vertex from standard form worksheets Grades 10–11

Find the vertex with x = −b ÷ 2a, then find y.

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How to do it

The vertex is at x = −b ÷ 2a. Put that x back in to find y.

y=x2+2x+9vertex: (−1,8)y = x^{2} + 2x + 9\quad \text{vertex: }(-1, 8)
−22(1)=−1\dfrac{-2}{2(1)} = -1x = −b ÷ 2a
y=(−1)2+2(−1)+9=8y = (-1)^{2} + 2(-1) + 9 = 8put x = −1 back in
vertex (−1,8);axis of symmetry x=−1\text{vertex }(-1, 8);\quad \text{axis of symmetry }x = -1

Example problems

  1. y=−2x2+4x+8vertex: y = -2x^{2} + 4x + 8\quad \text{vertex: }
  2. y=3x2+30x+87vertex: y = 3x^{2} + 30x + 87\quad \text{vertex: }
  3. y=−2x2+4x−4vertex: y = -2x^{2} + 4x - 4\quad \text{vertex: }
  4. y=−2x2+8x−18vertex: y = -2x^{2} + 8x - 18\quad \text{vertex: }

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