Quadratics are Second-Order Polynomials. which take on the form:
In this form:
A quadratic is referred to as a second-order polynomial since the highest exponent of \(x\) in a non-zero term is 2.
When a quadratic equation is represented visually, it is referred to as a parabola.
A quadratic function can be expressed algebraically in a few different ways:
This point acts as either the minimum or maximum point of a quadratic function.
The characteristics of the vertex depend on the sign of the \(x\) value in the quadratic equation:
We can make this process easier for ourselves by first creating a table of values to identify if there any intercepts:
Based on this table, we can determine that there aren't any x-intercepts, as there aren't any cells where \(y = 0\). However, we can determine that there is a y-intercept of \(3\), since \(y = 3\) when \(x = 0\).
To further confirm our results, we can graph this quadratic to get a better idea of how it looks visually. We will learn other techniques to find the x-intercepts soon.