Unit Four - Quadratic Relations Lesson 1 - Properties of Quadratics Learning Goals: - be able to state the properties of a parabola - be able to recognize a quadratic based on the graph, equation, or table of values - use the standard form of an equation to find properties of the parabola Let's Review...The Parabola opens down opens up Tables of Values Standard Form Opens down if a is negative. Opens up if a is positive. The Parabola Standard Form - Finding the Axis of Symmetry The axis of symmetry is a horizontal line. It has the equation, x = a, for some value a where the axis of symmetry would cross the x-axis. For an equation ax2+bx+c, the equation of the axis of symmetry is given by Example 1. What is the axis of symmetry of 2x2-3x+6? The vertex is on the axis of symmetry. Finding the vertex of a quadratic in standard form... Step 1) The axis of symmetry is given by x = a. Substitute the "a" into the equation for x. Step 2) Calculate the value for a subbed in for x. Step 3) The x-co-ordinate of the vertex is given by a. The y-co-ordinate of the vertex is given by the value that you get in Step 2). Example 2. Find the axis of symmetry and the vertex for the parabola below.