1. 3.3 Quadratic Functions Quadratic Function: 2nd degree polynomial
Graph is a parabola
Vertex (max or min)
Opens up or down
Has exactly one y-intercept
Can have 0, 1, or 2 x-intercepts

2. Axis of Symmetry: Vertical line through the vertex (h, k) that cuts the parabola in half.
A.S. x = h

3. Vertex Form: f(x) = a(x – h)2 + k (Transformation) vertex = (h, k)
Ex. 1 Find the vertex and the axis of symmetry of this quadratic. f(x) = -2(x – 3)2 – 7

4. Standard form: f(x) = ax2 + bx + c (polynomial) vertex = ( )
Ex. 2 Find the vertex of y = x2 – 2x + 3

5. To find the x-intercepts, let y = 0.
To find the y-intercept, let x = 0.
If +a, then parabola opens up.
If –a, then parabola opens down.

6. Find the vertex, axis of symmetry, & determine if the parabola opens up or down.
3a. g(x) = -6(x –2)2 – 5 Vertex: A.S.: Up or Down
3b. f(x) = 4(x +1)2 + 3 Vertex: A.S.: Up or Down

7. Find the x & y intercepts of each parabola
4a. f(x) = x2 + 8x – 1
y-int:
(x = 0)
x-int:
(y = 0)
4b. h(x) = -2(x+3)(x+1) y-int: x-int:

8. Write each equation in standard (polynomial) form. y = ax2 + bx + c
5a. g(x) = 2(x- 1)(x + 6)
5b. f(x) = 2(x + 3)2 - 4

9. Write the following functions in transformation (vertex) form
Write the following functions in transformation (vertex) form. f(x) = a(x – h)2 + k
6a. x2 + 4x – 5 = f(x)
6b. -(x – 4)(x+ 2) = f(x)