1. Parabolas

2. Graphing Parabolas Standard Form of a Quadratic Function
y=ax2+bx+c when a≠0
Find the vertex
Minimum
Maximum
Find the y-intercept

3. Properties y=ax2+bx+c When a>0 parabola opens up
When a<0 parabola opens down
Axis of symmetry is x=-b/2a
Vertex
x coordinate is –b/2a
y coordinate is found by substituting the x coordinate into the function
y-intercept is (0,c)

4. To Graph Find and graph the axis of symmetry Find and graph the vertex
Find and graph the y-intercept
Find and graph at least one other point on both sides of the axis of symmetry
Zero’s (x-intercepts) can be used
Sketch the curve

5. Ex1: y=x2-2x-3 axis of symmetry Other Points The vertex
Sketch the curve
y-intercept

6. Ex 2: y=-6x2-12x-1 Axis of symmetry Vertex y-intercept Two points
(-1, 5)
y-intercept
(0,-1)
Two points
(-1.91,0)
(-.09,0)
Sketch the curve

7. Ex 3: y=-4x2-24x-36 Axis of symmetry Vertex y-intercept Two points
(-3, 0)
y-intercept
(0, -36)
Two points
(-2,-4)
(-4,-4)
Sketch the curve

8. Translating Parabolas

9. Vertex Form y=a(x-h)2+k
h is how many the function has been translated horizontally
k is how many the function has been translated vertically
Vertex is (h,k)
Line of symmetry is x=h

10. Writing Equations in Vertex Form
A parabola has a vertex at (3,4) with the point (5, -4) on the parabola
h=3, k=4
Find a
y=a(x-h)2+k y=-2(x-3)2+4
-4=a(5-3)2+4
-4=4a+4
-8=4a
a=-2

11. Converting to Vertex Form
Find the line of symmetry (aka the x coordinate of the vertex)
Find the y coordinate of the vertex
Substitute into the vertex form equations
y=a(x-h)2+k

12. Ex: -3x2+12x+5 h = x= -12/2(-3) = -12/-6 = 2
k = y= -3(2)2+12(2)+5 = =17
y=a(x-h)2+k
y=-3(x-2)2+17

13. Practice Problems
P. 58
Choose 3 from # 1-9 Only find the vertex and state if it is a minimum or maximum
Choose 4 from # 21-29
P. 60
Choose 3 from # 1-6
Choose 3 from #7-12
Choose 4 from #19-27