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) variable) Opens

* 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 = ______