1Cademy - Finding the Maximum or Minimum Value of $$y = -4x^2 + 16x

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Minimum or Maximum Value of a Quadratic Equation

Example

Finding the Maximum or Minimum Value of $y = -4x^2 + 16x - 11$

To find the maximum or minimum value of the quadratic equation $y = -4x^2 + 16x - 11$ , determine the vertex of its parabola. Since the coefficient $a = -4$ is negative, the parabola opens downward, meaning it has a maximum value. The axis of symmetry is $x = -\frac{b}{2a} = -\frac{16}{2(-4)} = -\frac{16}{-8} = 2$ . Substitute $x = 2$ into the equation to find the $y$ -coordinate: $y = -4(2)^2 + 16(2) - 11 = -16 + 32 - 11 = 5$ . The vertex is (2, 5). Therefore, the maximum value of the quadratic equation is 5, which occurs at $x = 2$ .