GENERAL FORM
y = a√(b(x − h)) + k
a < 0
goes DOWN from vertex
b > 0
goes RIGHT from vertex
b < 0
goes LEFT from vertex
DOMAIN & RANGE
FACTORING
√(9x−18) = √(9(x−2)) = 3√(x−2)
Always factor before reading params!
GRAPHING STEPS
- Rewrite in std form y = a√(b(x−h))+k
- Identify a, b, h, k
- Plot vertex (h, k)
- Determine direction from signs of a and b
- Find y-intercept if graph heads toward origin
- Plot extra points, connect smoothly
INTERCEPTS
y-intercept
let x = 0, solve for y
x-intercept
let y = 0, isolate √, square both sides
Squaring can create extraneous solutions — always check!
FINDING THE RULE
- Read vertex → h and k
- Sketch to determine sign of b
- Substitute second point (x,y)
- Solve for a
- Write complete rule
Example: Vertex (−4,4), y-int = 10
b=+1 (right), 10=a√4+4, a=3
Rule: y = 3√(x+4)+4
INEQUALITIES
- Set y = c → find intersection point
- Sketch both graphs
- Read interval from graph
- Use interval notation for answer
COMMON MISTAKES
- Read AFTER factoring — not before
- In (x−h): (x+2) means h = −2
- Check domain before finding y-intercept