1. Solve:

2. Need Help? Look in textbook in Section 5.1: Modeling Data w/ Quadratic Functions Section 5.2: Properties of Parabolas Worksheet: Properties of Parabolas

3. Day 12: Properties of Parabolas on Graphs

4. Objectives: To identify properties of parabolas on graphs

5. A parabola is the shape created from the graph of a quadratic function (y = ax 2 + bx +c)

6. Direction: Parabolas open up or open down Open “up” “Smiling” Open “down” “Frowning”

7. Width: Parabolas can be narrow, standard or wide NarrowStandardWide

8. Axis of Symmetry: The line that divides the parabola into two parts that are mirror images The AOS is always a vertical line. All vertical lines have the equation x = #. The abbreviation for “Axis of Symmetry” is AOS. x = 2

9. Symmetry: Each point on the parabola has a corresponding mirror image. Each set of points is equidistant from the AOS.

10. Vertex: The point where the parabola passes through the AOS If the parabola opens up, the vertex is called a “minimum”. (0, -3) (2, 4) If the parabola opens down, the vertex is called a “maximum”.

11. y – intercept: The point on the graph where the parabola intersects the y-axis. Y – intercepts are always written as a point (0, #) (0, -3) (0, 0)

12. x – intercept(s): The point(s) on the graph where the parabola intersect the x - axis. Other names include: roots, zeroes and solutions. x – intercepts are always written as a point (#, 0) (0, 0) (4, 0) (2, 0) 2 Real Roots 1 Real Root No Real Roots Two Imaginary

13. Functions: Parabolas are functions because they pass the VLT

14. Domain: The domain of a parabola is (- ,  ) Range: Depends on how parabola opens, includes max or min and infinity. Always use bracket w/ #. D: (- ,  ) R: (- , 4] R: [-2,  )

15. Intervals of Rising/Falling: The interval of the domain where the graph is rising or falling as x increases Rising: ______________ Falling: _____________ “As x increases” means you read the graph like a book, from left to right. Parentheses are used because at the vertex the graph is neither rising nor falling.

16. Direction: _____________ Width: ______________ AOS: _________________ Set of corresponding points: _______________ Vertex: _______________ Max or Min? __________ y – int: _____________ x – int: _____________ Function? __________ Domain: ___________ Range: _____________ Rising: _____________ Falling: ____________ Opens up Wide (-2, -4) & (0, -4) x = -1 (-1, -4.5) Minimum (0, -4) (-4, 0) & (2,0) Yes (- ,  ) [-4.5,  ) (-1,  ) (- , -1)

17. Direction: _____________ Width: ______________ AOS: _________________ Set of corresponding points: _______________ Vertex: _______________ Max or Min? __________ y – int: _____________ x – int: _____________ Function? __________ Domain: ___________ Range: _____________ Rising: _____________ Falling: ____________ Opens down Narrow (0, -3) & (2, -3) x = 1 (1, 0) Maximum (0, -3) (1, 0) Yes (- ,  ) (- , 0] (- , 1) (1,  )

18. Name three of the properties you learned about today and how to find them.