MPM 2D Date: Quadratics Part 3 – Vertex Form Forms of Equations: 1. Standard Form y ax 2 bx c (Expanded Form) 2. Factored Form y a( x s )( x t ) Can determine the direction of opening Direction tells us whether we have a min or max Determine the zeros Determine the location of the vertex 3. Vertex Form y a( x h)2 k Determine the vertex by simple inspection Determine the ‘a’ knowing vertex and one other point Determine the direction of the opening by the value of ‘a’ Can convert to standard form by expanding and collecting like terms Remember: When a>0 When a<0 Equation Direction of Opening Relative Width (compare x2) Coordinates of Vertex y x2 y ( x 3)2 2 y 3( x 4)2 3 y 2( x 1)2 5 Working with Vertex Form 1. Given equation 1 y ( x 5) 2 3 2 a) State ‘a’ and the direction of opening b) What is the vertex Equation of Axis of Symmetry a h k MPM 2D Date: 2. Find, in vertex form, the equation of the quadratic relation with vertex at (5,-3) and passes through the point (1,-8). 3. Given equation y 2( x 3)2 7 a) If vertex is (-3,-7) find two other points on the parabola Hint: Choose a value for ‘x’ that is reasonably close to axis of symmetry, then substitute into the equation and solve for y.