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Solving Simple Quadratic Equations

Solving simple quadratic equations with examples: x² = k leading to x = ±?k, and x² - dx = 0 leading to x = 0 or x = d.

Courses Overview ? Video Tutorial Membership Required You must be a member of Math Angel Plus or Math Angel Unlimited to view this content. Join Now Solving Simple Quadratic Equations: For $x^2 = k$, there are two solutions: $x = pm sqrt{k}$. Note that $k$ must be non-negative, as $x^2$ cannot be negative. No Real […]

Solving Quadratic Equations by Factorising

Solving quadratic equations by factorising method step-by-step, note finding two numbers that multiply to the constant and add up to the coefficient of x.

Courses Overview ? Video Tutorial Solving Quadratic Equations by Factorising: To solve $x^2 + bx + c = 0$, find two numbers, $m$ and $n$, that multiply to the constant term $c$ and add to the coefficient $b$. Why Factorisation Method Works: Factorisation breaks down quadratic expressions into linear factors, making it easier to find […]

Solving Quadratic Equations: Quadratic Formula

Quadratic formula for solving quadratic equations, and the discriminant for determining the number of real roots.

Courses Overview ? Video Tutorial The Discriminant: The term $b^2 – 4ac$. A positive discriminant means two real roots, zero means one root, and a negative value means no real roots. Step-by-Step Examples: Identifying coefficients ($a$, $b$, $c$), substituting them into the quadratic formula, $x = small large frac{-b pm sqrt{b^2 – 4ac}}{2a}$, and calculating […]

Plotting and Reflecting Points on the Coordinate Plane

Plotting points on a coordinate plane with positive and negative coordinates.

Courses Overview ? Video Tutorial What is a Coordinate Plane?: The coordinate plane has two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), intersecting at the origin (0,0). Plotting Points on a Graph (Example): To plot a point like (2,1), locate 2 on the x-axis and 1 on the y-axis, then mark the intersection. […]

Expanding Double Brackets

Expanding double brackets showing the binomial product formula (a+b)(c+d)=ac+ad+bc+bd step-by-step.

Courses Overview ? Video Tutorial Membership Required You must be a member of Math Angel Plus or Math Angel Unlimited to view this content. Join Now Understanding Binomial Products: A binomial has two terms, such as $(a + b)$ or $(c + d)$. Multiplying two binomials forms a binomial product, $(a+b)(c+d)$. Expanding Double Brackets Example: […]

Square of a Binomial

Three binomial square formulas, including (a + b)² = a² + b² + 2ab, (a - b)² = a² + b² - 2ab, and (a + b)(a - b) = a² - b².

Courses Overview ? Video Tutorial Square of a Binomial Formula: $(a + b)^2 = a^2 + 2ab + b^2$. Geometric Interpretation: Visualising $(a + b)^2$ as the area of a large square, which is the sum of $a^2$, $b^2$, and $2ab$ (small rectangles within the square). Binomial Expansion – Minus Sign: $(a – b)^2 = […]

Simple Quadratic Equations

Quadratic equation formula y = ax² with a not equal to zero, highlighting coefficient 'a'.

Courses Overview ? Video Tutorial Membership Required You must be a member of Math Angel Plus or Math Angel Unlimited to view this content. Join Now Definition of Quadratic Equations: Quadratic equations contain an $x^2$ term; the standard form is $y = ax^2 + bx + c$ ($a neq 0$). Role of Coefficient $a$: The […]

Vertex Form and Parabola Transformations

Vertex form of quadratic equation y = a(x - h)² + k, showing the vertex at point (h,k) on a graph of a parabola.

Courses Overview ? Video Tutorial Vertex Form of Quadratic Equations: The vertex form is $y = a(x – h)^2 + k$, where $(h, k)$ is the vertex of the parabola and $a neq 0$. For example, in $y = 0.5 (x – 2)^2 – 3$, the vertex is $(2, -3)$. Vertex of a Parabola (The Turning […]

Converting Quadratics: General and Vertex Form

Converting quadratic equations between general form y = ax² + bx + c and vertex form y = a(x - h)² + k, where a ? 0.

Courses Overview ? Video Tutorial Converting Quadratic Equations: Learn to switch between the general form, $ax^2 + bx + c$, and the vertex form, $a(x – h)^2 + k$, (where $a neq 0$). Converting Vertex Form to General Form: Square the binomial, expand the brackets, and simplify to rewrite a quadratic equation in general form. […]

Simplifying Expressions with Multiple Variables

Simplification techniques for exponents showing multiplication rules with variables x and y, and explanation of the commutative law.

Courses Overview ? Video Tutorial Membership Required You must be a member of Math Angel Plus or Math Angel Unlimited to view this content. Join Now Expanding Brackets: If there are brackets, use the distributive law, multiply terms inside the brackets, and then use the simplification techniques. Simplifying Expressions Technique 1: Use exponents to simplify repeated […]