3.3 Q UADRATIC F UNCTIONS Objectives: Define three forms for quadratic functions Find the vertex and intercepts of a quadratic function and sketch its graph Convert one form of a quadratic function to another

Q UADRATIC F UNCTION : G RAPH M AKES A P ARABOLA S HAPE The rule of a quadratic function is a polynomial of degree 2. The rule? Polynomial of degree 2? Example: What can we say about parabola?

T HREE F ORMS OF W RITING A Q UADRATIC F UNCTION 1. Transformation form: 2. Polynomial form: 3. x-Intercept form: T RANSFORMATION F ORM * Most useful form for finding the vertex Vertex: (h,k) But how do we find the x and y intercepts? (x,0) (0,y)  Be careful

E XAMPLE 1:T RANSFORMATION F ORM

P OLYNOMIAL F ORM * Most useful for finding the y-intercept y-intercept: x-intercept: Vertex: (think of the transformation form) E XAMPLE 2: P OLYNOMIAL F ORM

X- INTERCEPT F ORM  H AS TO BE IN THIS F ORM * Mo st useful for finding the x-intercepts x-intercept: y-intercept: Vertex: E XAMPLE 3: X- INTERCEPT F ORM

S UMMARY AND C HANGING FROM O NE F ORM TO A NOTHER Changing to a polynomial: Expand Changing to a x-intercept: Expand and factor or use quadratic formula Changing to a transformation: Expand and complete the square

E XAMPLE 6: M AXIMUM A REA FOR A F IXED P ERIMETER A PPLICATIONS I NVOLVING F INDING V ERTEX 3.3 H MWR : P. 171: Q U :1,7,10, ODDCCCCC, 51