# How to Find the Maximum or Minimum Value of a Quadratic Function Easily

Four Methods:If the quadratic is in the form y = ax2 + bx + cIf the quadratic is in the form y = a(x-h)2 + kUsing differentiation when the quadratic is in the form y = ax^2 + bx + cExamples

The y-coordinate of the parabola's vertex (usually represented by k) is also the maximum or minimum value of the quadratic function represented by the parabola. Let's learn how to find it!

## Steps

### Method 1 If the quadratic is in the form y = ax^{2} + bx + c

- 1
**Decide whether you're going to find the maximum value or minimum value.**It's either one or the other, you're not going to find both.- The maximum or minimum value of a quadratic function occurs at its vertex.

For y = ax^{2}+ bx + c,**(c - b**gives the y-value (or the value of the function) at its vertex.^{2}/4a) - If the value of
**a**is positive, you're going to get the minimum value because as such the parabola opens upwards (the vertex is the lowest the graph can get) - If the value of
**a**is negative, you're going to find the maximum value because as such the parabola opens downward (the vertex is the highest point the graph can get) - The value of
**a**can't be zero, otherwise we wouldn't be dealing with a quadratic function, would we?

- The maximum or minimum value of a quadratic function occurs at its vertex.

### Method 2 If the quadratic is in the form y = a(x-h)^{2} + k

### Method 3 Using differentiation when the quadratic is in the form y = ax^2 + bx + c

- 1
**Differentiate y with respect to x.**dy/dx = 2ax + b - 2
**Determine the differentiation point values in terms of dy/dx.**Since dy/dx is the gradient function of a curve, the gradient of a curve at any given point can be found. Thus, the maximum/minimum value can be found by setting these values equal to 0 and find the corresponding values. dy/dx = 0, 2ax+b = 0, x = -b/2a - 3
**Substitute this value of x into y to get the minimum/maximum point.**

### Method 4 Examples

## Tips

- The parabola's axis of symmetry is x = h.
- -h is the value that corresponds to your maximum or minimum value.

## Article Info

Categories: Algebra