1. What is a parabola? Do Now: Answer the aim to the best of your ability.

2. What is the technical definition of a parabola  A parabola is the locus of all points equidistant from a fixed point called focus and a fixed line called the directrix.  The focus is a point on the axis of symmetry.  The directrix is a fixed line.  A parabola is the locus of all points equidistant from a fixed point called focus and a fixed line called the directrix.  The focus is a point on the axis of symmetry.  The directrix is a fixed line.

3. What is the equation of a parabola?  There are two forms of the equation  Standard form: y=ax 2 +bx+c  Vertex form: y=a(x–h) 2 +k  We are going to be working with the vertex form.  In the vertex form, (h,k) is the vertex of the parabola, and we can use the equation to find the focus and directrix.  There are two forms of the equation  Standard form: y=ax 2 +bx+c  Vertex form: y=a(x–h) 2 +k  We are going to be working with the vertex form.  In the vertex form, (h,k) is the vertex of the parabola, and we can use the equation to find the focus and directrix.

4. How do we convert from standard form to vertex form?  We need to find a, h, and k.  To find a…  Ummmm…just look at the equation, it is the same.  To find h…  h, the x-value of the vertex can be found using the formula h=–b/2a  To find k…  Substitute x in the original equation with the h-value we found.  The resulting value is k  We need to find a, h, and k.  To find a…  Ummmm…just look at the equation, it is the same.  To find h…  h, the x-value of the vertex can be found using the formula h=–b/2a  To find k…  Substitute x in the original equation with the h-value we found.  The resulting value is k

5. Convert from standard to vertex form. y=x 2 –6x+13 y=x 2 +4x+3 y=3x 2 +6x+8 y=x 2 –6x+13 y=x 2 +4x+3 y=3x 2 +6x+8

6. How do we find the focus and directrix of a parabola?  If we have the vertex form of a parabola, we can easily find the focus and directrix.  The focus is located at the point (h, k+1/4a).  The directrix can be described by the equation y=k–1/4a.  If we have the vertex form of a parabola, we can easily find the focus and directrix.  The focus is located at the point (h, k+1/4a).  The directrix can be described by the equation y=k–1/4a.

7. Find the focus and directrix. y=(x–3) 2 +4 y=(x+2) 2 –1 y=3(x+1) 2 +5 y=(x–3) 2 +4 y=(x+2) 2 –1 y=3(x+1) 2 +5

8. Try on your own  Which of the following equations has a vertex of (3, –1) and a focal point of (3, 1/2)? (1) y = (x–3) 2 + 1 (2) y = (x+3) 2 – 1 (3) y = (1/6)(x–3) 2 – 1 (4) y = (1/2)(x–3) 2 + 1  Which of the following equations has a vertex of (3, –1) and a focal point of (3, 1/2)? (1) y = (x–3) 2 + 1 (2) y = (x+3) 2 – 1 (3) y = (1/6)(x–3) 2 – 1 (4) y = (1/2)(x–3) 2 + 1

9. Homework  pg 175, #5, 6, 8, 16-20