Skip to content# Turning Point Quadratic Equation Calculator

Quadratic Equation Calculator

Ever the values of **“a” , “b” & “c”** for the general quadratic equation **ax ^{2} + bx + c. The Calculator will give you the values of the Turning Point and Roots of the Quadratic Equation**

Turning Point: (?, ?)

Roots: ?

**Turning Point of a Quadratic Equation**

**What is Turning Point of Quadratic Equation?**

**The turning point of a quadratic equation**, also known as the vertex, is the point on the graph of the quadratic function**where the graph changes direction.**

- This point represents either the
**maximum or minimum value of the quadratic function,**depending on the direction in which the parabola opens.

For a quadratic equation in the form

$y=a{x}^{2}+bx+c$, the turning point can be found using the formula:

where a, b, and c are constants, and x represents the variable. Quadratic equations often depict parabolic curves when graphed, showcasing a symmetrical arc that either opens upwards or downwards.

$x=\frac{-b}{2a}$

- The x-coordinate of the turning point, $\frac{-b}{2a}$
, is the axis of symmetry for the parabola.

- The y-coordinate, $f\left(\frac{-b}{2a}\right)$
, represents the maximum or minimum value of the quadratic function.

**If ‘a’ is positive, the parabola opens upward, and the turning point is the minimum.****If ‘a’ is negative, the parabola opens downward, and the turning point is the maximum.**

- The graph of quadratic equation represents a parabola, which can look something like this: curving either upward or downward

Our goal is to locate the **turning point of this parabola.**

- if your coefficient
**“a > 0”**, then it represents the lowest point on the parabola, and if your coefficient**“a < 0”**, it represents the highest point of the parabola.

**Thus we can say:**

The turning point **is a crucial concept when analyzing and graphing quadratic equations**, as it provides information about the highest or lowest point on the parabolic curve.