This document discusses analyzing quadratic functions of the form y = a(x - p)2 + q. It provides examples of determining the vertex, domain and range, direction of opening, axis of symmetry, and x- and y-intercepts of quadratic functions.

1. 11P.R.3
Analyze quadratic functions of
2
the form y = a (x – p) + q and
determine the
• vertex
• domain and range
• direction of opening
• axis of symmetry
· x - and y -intercepts

2. Vertex
y = 67(x-3)2-6 v: (3,-6)
y = -3 (x + 2) 2 + 10 v: (-2, 10)
y = (x + 67) 2 - 18
v: (-67, -18)

3. Domain and Range
2
y = 3(x+4) + 6
Domain = { <x< }
( , )
Range: {6 x < }
[6, )

4. Direction of Opening
2
y = 3(x+4) + 6 up
2+6
y = -3(x+4)
down

5. Axis of Symmetry
y = 67(x-3)2-6
x=3

6. x and y intercepts
x intercept is where the line crosses
the x axis, (y = 0)
y intercept is where the line crosses
the y axis, (x = 0)

7. x intercept
2 + 27
y = -3 (x + 2)
y=0
0 = -3(x + 2) 2 + 27
2
-27 = -3(x+2)
-27/-3 = (x+2)2
9 = (x+2) 2
9=x+2 x intercept = 1 and -5
3 = x +2 (1,0) & (-5,0)
x = 1 or -5

8. y intercept
2 + 27
y = -3 (x + 2)
x=0
2 + 27
y = -3(0+2)
y = -3(4) + 27
y = -12 + 27
y = 15
y intercept = 15
(0,15)