An introduction to quadratic equations and rules for simplifying quadratic equations.
Graphing a quadratic equation by plotting many points on the line. All quadratic equations have an axis of mirror symmetry and a minimum or maximum point.
We discuss the transformations, vertical shift, reflection, and stretch.
The solutions, axis of symmetry, and vertex of a quadratic equation where b=0.
The solutions can be found by first factorising the equation.
Factorising a quadratic equation explained geometrically.
Finding the solutions, axis of symmetry, and vertex of a factorisable quadratic equation.
We discuss how to design a quadratic equation by placing the solutions and vertex.
Perfect quadratic squares have equals solutions and the curve touches the x-axis
Transformation of a quadratic equation such as stretch, reflection, vertical and horizontal displacment are explored.
We discuss completing the square for quadratic equations to find the solutions.
Completing the square shows that all quadratic curves can be formed by applying transformation to the simplest quadratic curve y=x²
The quadratic formula is derived step by step by completing the square of the quadratic equation y=ax²+bx+c. This sections does not contain any exercises.
The quadratic formula can be used to find the solutions of any quadratic equation. The number of solutions is determined by the sign of the descriminant. A quadratic graph with no solutions does not cross the x-axis, and graphs with one solution touches the x-axis at one point.