PARABOLAS Topic 7.2

Definition The set of all points in a plane that are the same distance from a given point called the focus and a given line called the directrix.

Writing linear equation in parabolic form GOAL: Turn general form Standard form

Writing linear equation in parabolic form Start with Group the two x-terms Pull out the constant with x2 from the grouping Complete the square of the grouping **Look back to Topic 6.3 for help** Write the squared term as subtraction so that you end with standard form

Group x-terms Pull out GCF Complete the Square **Remember that whatever you add in the grouping must be subtracted from the c-value** Factor and simplify

Summary of Parabolas in Standard Form Equation Axis of symmetry x = h y = k Vertex (h, k) Focus Directrix Direction of opening Up: a>0, Down: a<0 Right: a>0, Left: a<0 Latus Rectum

Graph of prior example

You Try!! Write the following equation in parabolic form. Then identify all of the parts. Vertex: (5, -32) Focus: (5.25, -32) Axis of Symmetry: Latus Rectum: 1 X=5 Direction of Opening: Right Directrix: x= 4.75