MathAlgebraHigh frequency

SAT Math: Finding the Vertex from Standard Form

29+ practice questions in Praczo

What you need to know

The concept, explained

  • 1

    For a quadratic in standard form y = ax² + bx + c, the x-coordinate of the vertex is x = -b / (2a).

  • 2

    To find the y-coordinate (the minimum or maximum value), plug the x-coordinate back into the equation.

  • 3

    If a > 0, the parabola opens upward (the vertex is a minimum). If a < 0, it opens downward (maximum).

  • 4

    This method is often much faster than completing the square, especially when the SAT only asks for the x-coordinate.

  • 5

    The axis of symmetry is the vertical line passing through the vertex: x = -b / (2a).

Common mistakes
  • Forgetting the negative sign in the formula (-b/2a).
  • Thinking the x-coordinate is the minimum/maximum value itself (the y-coordinate is the actual value, x is just where it occurs).
Try a sample question

SAT-style practice

At what value of x does the function f(x) = -2x² + 12x - 5 reach its maximum value?

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