**Quadratic equations**

A quadratic equation is an equation that has one term with a variable of a power of *2* . All quadratic equations are in the form of

where* a* is a second degree term coefficient,

**b***is a first degree term coefficient and*

*is a constant term.*

**c****Example 1**

Let us first look at an incomplete quadratic equation that lacks a first degree term, *i.e. b = 0*

The property of a zero-product

If the product of two terms is zero, then either of the terms is zero or both of the terms are zero.

**Example 2**

Another incomplete quadratic equation is one that lacks a constant term, that is,* c = 0*

**The ****Quadratic ****F****ormula**

**The**

**Quadratic**

**F**

**ormula**

In a complete quadratic equation, we need a quadratic formula to solve the equation. That is, where all the coefficients* a*,

*and*

**b***are different from*

**c***0*.

Example 3

Solve the quadratic equation using the quadratic formula

We collect the coefficients and remember that the sign is included with the number

*a = 1, b = -2* and* c = -8*

these are substituted into the formula

So the solutions are *x = -2* or* x = 4*

## The graph of a quadratic function

The graph of the quadratic function is a parabola. The second degree term coefficient determines whether the parabola opens upwards or downwards. When *a> 0* parabola opens upwards. When *a <0* the parabola opens downwards. If *a = 0*, then this is not a second degree polynomial function because there would be no second degree term.

Below is the graph of the function* f*. The graph intersects the* x*-axis at *x = -1* and *x = 5*. These would be the answer for the quadratic equation *f(x)=0*

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