Warm-up!!

Parabolas

Parabolas Parabola: the set of points in a plane that are the same distance from a given point called the focus and a given line called the directrix. The cross section of a headlight is an example of a parabola... The light source is the Focus Directrix

Here are some other applications of the parabola...

Notice that the vertex is located at the midpoint between the focus Directrix Notice that the vertex is located at the midpoint between the focus and the directrix... Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... We can determine the coordinates of the focus, and the equation of the directrix, given the equation of the parabola....

Standard Equation of a Parabola: (Vertex at the origin) Equation Focus Directrix (x-h)2 = 4p(y-k) (h, k+p) y = k–p (If the x term is squared, the parabola is up or down) Equation Focus Directrix (y-k)2 = 4p(x-h) (h+p, k) x = h–p (If the y term is squared, the parabola is left or right)

Tell whether the parabola opens up down, left, or right.

Find the focus and equation of the directrix. Then sketch the graph. Direction: Opens right P= 4

Find the focus and equation of the directrix. Then sketch the graph. Direction: Opens up P= 1/2

Find the focus and equation of the directrix. Then sketch the graph. Direction: Opens down P= -3

Find the focus and equation of the directrix. Then sketch the graph. Direction: Opens left P= -1

Find the focus and equation of the directrix. Then sketch the graph. 5: (y – 2)2 = -16 (x - 5) Direction: Opens left P= -4

Find the focus and equation of the directrix. Then sketch the graph. Direction: Opens up 6. (x – 8)2 = 8(y + 3) P= 2

Writing Equations of Parabolas In Standard Form

Write the equation in standard form by completing the square. State the VERTEX & DIRECTION.

8. Write the equation in standard form by completing the square. State the VERTEX & DIRECTION.

YOU TRY # 7 & #8