How to Find the Turning Point for a Quadratic Graph

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The derivative is a handy tool for finding the turning point on a graph of a quadratic function. To find whether the turning point is a minimum or maximum, take the second derivative of the function. If the result is greater than zero, the turning point is a minimum. If it is less than zero, the point is a maximum. For the point itself, take the first derivative of the equation with respect to x. Set the result equal to zero and solve for x. Substitute the solution into the original equation and solve for y.

Things You'll Need

  • Pencil and paper
  • Calculator
  • Write down the equation for the quadratic graph.

  • Get the equation into the form of ax^2 + bx + c = y, if necessary. For example, if the equation is 2x^2 + 5x = y + 3, then it becomes 2x^2 + 5x -- 3 = y.

  • Take the first derivative of the equation with respect to x. In this case, the derivative is 4x + 5 = 0.

  • Solve for x using algebra. In this example, 4x + 5 = 0, 4x = 5, x = 5/4.

  • Substitute the value of x into the original equation and solve for y.

    2(5/4)^2 + 5(5/4) --3 = 6 3/8. The turning point is (5/4, 6 3/8) or (1.25, 6.375).

References

  • Photo Credit Jupiterimages/Photos.com/Getty Images
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