Write the quadratic as y = ax^2 + bx + c. For the function to be a quadratic, "a" -- the coefficient of x^2 -- must not be equal to zero. Suppose you have the equation y = -4x^2 + 3x + 8.
Determine if the parabola opens up or down. If "a" is greater than zero, the parabola opens up, and the maximum point is infinity. If "a" is less than zero, the parabola opens down and the vertex formula is used to find the coordinates of the maximum point. In this case, "a" equals -4. Therefore, the vertex formula can be used to find the maximum.
Use the formula vertex = -b/2a to find the x-value of the maximum. In this case, the x-value is -3/(2 * (-4)), which equals 0.375.
Substitute the x-value from Step 3 in the equation of the function to determine the y-value of the vertex. Substituting the x-value in y = -4x^2 + 3x + 8 gives -4 * (0.375^2) + 3 * 0.375 + 8, which equals 8.562.
Write the coordinates of the vertex in the form (x, y) to get the maximum point of the quadratic. In this example, the maximum is given by the point (0.375, 8.562).