How to Write Quadratic Equations in Vertex Form and Standard Form

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(0:01) How to Write Quadratic Equations Using Vertex Form: When the vertex $(h, k)$ is known, substitute directly into the vertex form, $y = a(x – h)^2 + k$, and use an additional point to solve for $a$.
(1:08) How to Write Quadratic Equations Using Standard Form: For cases without a known vertex, use the general form $y = ax^2 + bx + c$ by plugging in three points to form three equations, then solve for $a$, $b$, and $c$.
(2:04) Applying Quadratic Equations to Real-Life Scenarios: Use quadratic equations to represent a tunnel’s height, and assess if a lorry can pass.

📂 Revision Cards

Quadratic equations with vertex form y = a(x - h)² + k and general form y = ax² + bx + c, labelled as methods for forming quadratic equations. — 1) Quadratic Equation Formulas

Forming a quadratic equation using vertex form with equation y = -2(x - 2)² + 3, where the vertex is (2,3) and the curve passes through (3,1). — 2) Write Quadratic Equations in Vertex Form

Forming quadratic equations using the general form y = 2x² - x + 3, solving coefficients with three given points: (0,3), (1,4), and (2,9). — 3) Form Quadratic Equations in Standard Form

Solving the classic tunnel problem. The parabola equation is y = -5/9 · x² + 5 and the vertex is at (0,5). When x = 1, the truck can pass through. — 4) Quadratic Equation Application

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