Quadratic Functions

Quadratic equation in general form

where a, b and c are constants and a ≠ 0

Solutions or roots of the quadratic equation ax2+bx+c=0

x-coordinates of the intersection points between the graph y=ax2+bx+c and the x-axis

Methods used to solve quadratic equations

-Completing the square -Formula

If α and β are the roots of a quadratic equation, then x^2 – (α + β)x + αβ = 0

For x2 – (α + β)x + αβ = 0, α + β is the sum of roots and αβ is the product of roots

Quadratic inequality in one variable

An inequality with a quadratic expression on one side and zero on the other side

Three methods which can be used to solve a quadratic inequality

-graph sketching -number line -table methods

A quadratic equation in the form of (x − a)(x − b) = 0, where a < b

-if (x − a)(x − b) > 0, then x < a or x > b -if (x − a)(x − b) < 0, then a < x < b

Two different real roots

Two equal real roots

No real roots