Chapter 3 Review Quadratic Equations

1. Chapter 3 ReviewQuadratic Equations

2. Properties of Quadratics (Parabolas) • direction of opening: if a parabola opens up it has a U-shape, down it has a upside down U- shape. • vertex: the highest / lowest point on the parabola • axis of symmetry: the line of symmetry on the parabola this vertical line passes though the vertex • zeros/roots: the point(s) where the parabola passes through the x-axis

3. Example: • The direction of opening ______ • The vertex is (____, ____) • The axis of symmetry is x = ______ • The zeros are (____,____) and (____,____)

4. Different Forms of the Parabola Equations FACTORED STANDARD VERTEX FORMFORMFORM s and t are zeros a is the direction vertex is (h,k) • a is direction ofof opening a is direction of opening opening

5. Expanding • Multiply everything in one bracket by everything in another. Example 1 Example2

6. Factoring • Technique 1: Common Factoring • Technique 2: Simple Trinomial

7. Technique 3: Decomposition • Technique 4: Diff of Squares

8. Finding the Vertex • Method 1: Calculate the zeros, axis, vertex • Example • Determine the vertex , use this information to graph Factor (if necessary) to get equation into factored form If equation is already factored skip this step

9. Set each term equal to zero and solve to get the zeros Calculate the axis by adding the zeros and then dividing by 2

10. Sub the axis into the equation to get the y-coordinate of the vertex • Vertex is

11. Chapter 3 Review Questions