1. Warm Up Important Properties: 1.The graph will open up if ‘a’ ___ 0 and down if ‘a’ ___ 0 3.The vertex formula for: vertex format is: standard format is: 4.What equals 0 for the y intercept 5.What equal 0 for the x intercept

2. Graph Quadratic Functions in Intercept Form By the end you should: graph quadratics in intercept form Quadratic Function Terms: Intercept Form: y = a(x – p)(x – q) Parabola: graph of quadratic function

3. Graph the following parabolas. Include 3 points, label the vertex, and show the axis of symmetry with its line equation. 1. Opens up or down? a= b= c= vertex = y-intercept =

4. 2. Opens up or down? a= b= c= vertex = y-intercept =

5. Intercept Form 1.x-intercepts are p and q so... (p, 0) and (q, 0) 2. axis of symmetry half way between p and q: x = p + q 2 3.opens up if ‘a’ is positive and down if ‘a’ is negative Graph the following functions: Label the vertex, x-intercepts, and axis of sym. 1. x-int: vertex: find x  p + q 2 find y 

6. x-int: vertex: find x p + q 2 find y int 3.

7. REVIEW: Graphing the Intercept Form of a Parabola Intercept Form: y = a (x - p) (x - q) The graph of this is the y = ax 2 shifted so that the graph crosses the x-axis at p and q. –Characteristics of intercept form are: x-intercepts are p and q Axis of symmetry is halfway between (p, 0) and (q, 0) x= (p + q) / 2 If a>0 it opens up, if not then it opens down. Graph is wide if |a| 1

8. Converting Back to Standard Form To convert it back into Standard Form: –Multiply equation out using PEMDAS and FOIL (First-Outside-Inside-Last) –Combine like terms –Keep y on one side and the rest on the other. Vertex Form: y = a( x-h) 2 + k Intercept Form: y = a (x - p) (x - q) Standard Form: y = ax 2 + bx + c

9. 1. Write in standard form 2. Write in standard form

10. Exit Card 4.1-2 Give me 5! 1.y = x² + 10x + 21 What is the y-intercept? 2.y = (x – 2)² – 1 What is the vertex? 3.y = 3(x – 1)(x – 4) What are the x-intercepts? 4.y = 3 (x – 3)² – 3 What is the vertex? 5. What is the minimum or maximum value of the function in #4?