CCGPS Geometry Unit 9 – Modeling Geometry 9.3 – Notes Name: ________________________________________________ Date: _______________________ Graphing Parabolas as Conic Sections – Notes Parabolas can open 4 different ways: l l l l A parabola is like a line that has bent around a FOCUS POINT. You will need to know how to be able to identify the: • vertex • p-value • focus • focal width • directrix You will need to find p in order to find two of those items. p is the distance from the vertex to the focus and the distance from the vertex to the directrix. These parabolas will graph wider than usual. Focus Directrix (Always ADD p to (Always SUBTRACT p Graph Equation Vertex the non-squared to the non-squared Focal Width variable) Opens variable) * 1 2 ⎛⎞ (y – k) = (x – h) ⎜⎟h,k (h, k + p) y = k – p FW = |4p| Up or Down 4p ⎝⎠ * 1 2 ⎛⎞ (x – h) = (y – k) ⎜⎟h,k (h + p, k) x = h – p FW =|4p| Right or Left 4p ⎝⎠ When x is squared: • If p is ____________________ the parabola opens ________________. • If p is ____________________ the parabola opens ________________. When y is squared: • If p is ____________________ the parabola opens ________________. • If p is ____________________ the parabola opens ________________. CCGPS Geometry Unit 9 – Modeling Geometry 9.3 – Notes Graphing Parabolas: 1. Find the p-value by dividing the denominator by 4. 2. Determine which way the graph will open (up, down, left, or right). 3. Find the VERTEX (h, k) and plot it. 4. Depending on the way the parabola opens, use the p-value to graph the DIRECTRIX and FOCUS. 5. Plot the 2 points for the Focal Width from the Focus. FW = |4p| Find the value of p, vertex, FW, focus, directrix, and then draw the graph. 1 2 1. yx+=14 − 12 ( ) p = ________ Graph Opens: __________ Vertex: _________ Focus: _________ Directrix: __ = _______ Focal Width = _______ 1 2 2. xy+=13 − 8 ( ) p = ________ Graph Opens: __________ Vertex: _________ Focus: _________ Directrix: __ = _______ Focal Width = _______ CCGPS Geometry Unit 9 – Modeling Geometry 9.3 – Notes 1 3. yx=− 2 12 p = ________ Graph Opens: __________ Vertex: _________ Focus: _________ Directrix: __ = _______ Focal Width = _______ 1 2 4. xy−52=− − 16 ( ) p = ________ Graph Opens: __________ Vertex: _________ Focus: _________ Directrix: __ = _______ Focal Width = _______ .