You should be aware that the general equation of a quadratic is y = ax² + bx + c and the general equation of a cubic is y = ax³ + bx2 + cx + d. At bronze level we learn how to determine quadratic equations of the form y = ax(x + b). Silver level shows us how to write quadratic equations in the form y = k(x + a)(x + b). We finish up with the gold section where we learn how to write cubic functions in the form y = k(x + a)(x + b)(x + c).

Video 75: Outcome 1 - Writing quadratic functions in the form y = ax(x + b). Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 76: Outcome 2 - Writing quadratic functions in the form y = k(x +a)(x + b). Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 77: Outcome 3 - Determining the equation of a cubic function. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

Knowing how to complete the square from National 5 is ESSENTIAL prior knowledge before we begin. At bronze and silver level we learn how to complete the square for non-unitary x² when it is positive (quite straight forward) or negative (not so straight forward!). Well worth a watch!

At gold level we learn how completing the square can help us to find the maximum or minimum values of functions and the corresponding values of x when they occur.

Video 78: Outcome 1 - Completing the square for positive, non-unitary x². Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 79: Outcome 2 - Completing the square for negative, non-unitary x². Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 80: Outcome 3 - Maximum and minimum values of a quadtratic function. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

At bronze and silver level we learn how to solve quadratic inequalities by removing a common factor and by factorising simple trinomials. If you're rusty on factorising you MUST revise this skill from the National 5 Online Learning Portal first in Expressions & Formulae 1.2b.

At gold level we look at solving quadratic inequalities by factorising trickier trinomials. This skill is a very important one to learn as not only can it appear as a stand alone question but can also be dropped into questions from many other topics, i.e. suggesting suitable domains, finding a range of values which represent a circle, increasing/decreasing functions, etc.

Video 81: Outcome 1 - Solving a quadratic inequality with a common factor. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 82: Outcome 2 - Solving a quadtratic inequality with unitary x². Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 83: Outcome 3 - Solving a quadtratic inequality with non-unitary x2. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

Before attempting this module you MUST revise how to calculate the discriminant and use this to determine the nature of the roots of a quadratic if you need to. You'll find questions to try in the National 5 Online Learning Portal --> Relationshipps --> 1.3b. At bronze and silver level in this module we learn how to solve for equal, real and no real roots.

At gold level we develop our skills with some tricky algebra. Well worth a watch!

Video 84: Outcome 1 - Solving for equal roots. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 85: Outcome 2 - Solving for real or no real roots. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 86: Outcome 3 - Solving for equal, real or no real roots with hard algebra! This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

At bronze level in this module we learn how to find the points of intersection between a parabola and a straight line. At silver level, we discover how to show that a line is a tangent to a curve and how to find the coordinates of the point of contact.

At gold level, we learn how to show that a line does not intersect a parabola. Well worth a watch!

Video 87: Outcome 1 - 2 points of contact. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 88: Outcome 2 - 1 point of contact. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 89: Outcome 3 - No points of contact. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?