A quadratic equation is an equation that has in one term, a variable with 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.
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.
Another incomplete quadratic equation is one that lacks a constant term, that is, c = 0
he 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.
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
is substitute in to the formula
So the solutions are x = -2 or x = 4
Making a binomial square
A quadratic equation can also be solved by squaring. That is, we build the square of the binomial to the left of the equation.
Solve by squaring
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 the 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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