1. Lesson 10-1 Parabolas & Quadratic Equations

2. Definition of a Parabola
Definition of a Parabola
A parabola is the set of all points in a plane equidistant from a fixed point and a line.
The fixed point is called the focus.
The line is called the directrix.
Distances from a point to a line are always measured perpendicular to the line.

3. Characteristics of Parabolas
The focus always lies on the inside of the parabola.
𝑝 is the distance from the vertex to the focus. This is called the focal length.
The same distance, but on the other side of the vertex is a line called the directrix.
The axis of symmetry passes through the vertex and focus and is perpendicular to the directrix.
The direction of the axis of symmetry is determined by which variable is squared.

4. Graph each of the following parabolas
Graph each of the following parabolas. Also state the vertex, focus, directrix, and axis of symmetry.
𝑦=− 𝑥

6. Graph each of the following parabolas
Graph each of the following parabolas. Also state the vertex, focus, directrix, and axis of symmetry.
𝑥+2= 𝑦−1 2

8. Graph each of the following parabolas
Graph each of the following parabolas. Also state the vertex, focus, directrix, and axis of symmetry.
𝑥= − 1 8 𝑦−

9. Graph each of the following parabolas
Graph each of the following parabolas. Also state the vertex, focus, directrix, and axis of symmetry.
𝑦+3= 𝑥−2 2

10. Use the given information to write the equation of the parabola.
a.) Vertex: (3,4); Focus: (3,6) b.) Vertex: (−2,1); Directrix: 𝑦=4 c.) Focus: (−4,0); Directrix: 𝑥=4 d.) Focus: (5,7); Directrix: 𝑦=3