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 c is a constant term.

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 Formula

In a complete quadratic equation, we need a quadratic formula to solve the equation. That is, where all the coefficients a, b and c are different from 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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