Convert equations of parabolas from general to vertex form

Learning Objectives Identify the general and vertex forms of a parabola's equation. Explain the algebraic process of 'completing the square'. Convert the equation of a vertical parabola (y = ax² + bx + c) from general form to vertex form. Convert the equation of a horizontal parabola (x = ay² + by + c) from general form to vertex form. Determine the vertex (h, k) and direction of opening from the vertex form. Solve problems involving the conversion of parabolic equations, especially when the leading coefficient 'a' is not 1. Ever wondered how a satellite dish focuses signals to a single point or how a basketball player makes a perfect shot? 🏀 The secret lies in the precise geometry of parabolas! This tutorial will teach you a powerful algebraic tec...

TermDefinitionExample General Form (Vertical Parabola)An equation of a parabola written as y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.y = 2x² - 8x + 5 Vertex Form (Vertical Parabola)An equation of a parabola written as y = a(x - h)² + k, where (h, k) is the vertex of the parabola.y = 2(x - 2)² - 3 General Form (Horizontal Parabola)An equation of a parabola written as x = ay² + by + c, where a, b, and c are constants and a ≠ 0.x = -y² + 6y - 4 Vertex Form (Horizontal Parabola)An equation of a parabola written as x = a(y - k)² + h, where (h, k) is the vertex of the parabola.x = -(y - 3)² + 5 VertexThe turning point of a parabola. It is the minimum point if the parabola opens upwards or rightwards, and the maximum point if it opens downwards or leftwards.For the parabola y =...

Vertex Form of a Vertical Parabola y = a(x - h)² + k Use this form to quickly identify the vertex (h, k) of a parabola that opens up or down. If a > 0, it opens up. If a < 0, it opens down. Vertex Form of a Horizontal Parabola x = a(y - k)² + h Use this form to quickly identify the vertex (h, k) of a parabola that opens right or left. If a > 0, it opens right. If a < 0, it opens left. Note that h and k are switched compared to the vertical form. The 'Completing the Square' Term For an expression x² + bx, the term to add is (b/2)². This is the core calculation for the conversion process. Find the coefficient of the linear term (b), divide it by 2, and square the result. This value creates a perfect square trinomial.