Chapter 2: Quadratics

The discriminant

B²-4ac

If discriminant =0

One discrete solution/ two equal solutions

If discriminant>0

Then there are two equal solutions

If discriminant <0

There are no real solutions

Equation of Quadratic

typically in the form ax² + bx + c = 0, where a, b, and c are coefficients.

Shape of quadratic

A parabola, opening upwards if a > 0 (positive-U) and downwards if a < 0. (negative-n)

What are the three ways to solve a quadratic

• factorising

• completing the square

• quadratic formula

Quadratic formula

-b±√(b²-4ac) / 2a

Completing the square

A method used to solve quadratic equations by rewriting it in the form (x - p)² + q, making it easier to find the roots.

How do we complete the square

-half b , then minus square of that number

What to do when completing square if there is a coefficent of a in the quadratic

Divide the entire equation by a before completing the square.

OR if there’s not a factor,factor out up to +C and complete square as normal then add factor back in by multiply the +q bit by it

How can we find turning point(min/max)

completing the square.

(-p,q) -change sign of p q stays same

Psuedo quadratic

A type of function that resembles a quadratic equation but does not satisfy all the properties of a true quadratic, often involving terms that do not follow the standard form.

x⁶ + 9x³ + 8 = 0

How do we deal with psuedo quadratics

This involves rewriting the function in a way that allows us to analyze it as a quadratic or examining its behaviour through transformation techniques, even if it does not fit the standard quadratic form. e.g let x³ =y