C1- Algebra and Functions - Quadratic Functions

Now we learn about Quadratic Functions. They're arguably one of the most important types of functions, and you will need to be able to solve them and master the concept, as they will pop up later in other modules. A Quadratic equation, have a degree of 2, takes the form :

ax^2 + bx + c = 0 , where a,b,c are real numbers.

We can solve, quadratic equations using three methods : a) Factorisation, b) Completing the Square and c)The Quadratic Formula.

Quadratic Functions when sketched are of a parabola shape ( a U shape), the coefficient of x^2 will decide the shape of the parabola. If a is negative, the shape will be an upside down U, if positive it will be a U.

The solutions of a quadratic equations are called ROOTS. If you're dealing with a quadratic inequality we call the roots (CRITICAL VALUES).

1) Factorisation... Let ax^2 + bx + c = 0

find two numbers that multiply to give c , and add to give b. (These numbers must be the same for the product and sum)
*Make sure you take care, when you have negative numbers. (Remember a negative * negative = positive)

If you find two numbers that satisfy the product for c, and sum of b: simply put it in the form :

(x + ...) (x + ...) = 0  (... are the two numbers, it does not matter which order they are put)

To find the solution simply put (x +...) = 0, for both of them and solve for x. I shall provide an examples on my
handwritten image.