1. Chapter 4 Review

2. What shape does a Quadratic Function make What shape does a Quadratic Function make when it is graphed? when it is graphed?1. 2. What does it mean to solve a quadratic equation? Parabola—a “u-shaped curve 3. Name the 3 methods you can use to solve a quadratic equation. equation. Find x-intercepts GraphFactor Quadratic formula Power of the calculator baby! Graph!

3. Chapter 4: Quadratic Functions An infinite number of points that fall along a curved shape called a parabola. curved shape called a parabola. Two variable equation: (when the ‘x’ variable has an exponent = two)

4. Your Turn: 4. Describe the transformation to the parent function: 5. Describe the transformation to the parent function: translated up 3 translated left 5 2 times as steep translated right 1 6. Describe the transformation to the parent function: Reflected across x-axis 1/2 as steep translated up 4 translated left 3

5. Vertex Form: Vertex is (h, k) (h, k) What is the vertex? -h = -3 h = 3 k = 2 k = 2 Vertex is (3, 2) (3, 2) Think transformation: Vertex (0,0) has been moved right 3 and up 2. New vertex: (3, 2)

6. Vertex Your turn: What is the vertex ? 8. 9. 7.

7. Axis of symmetry 1 5 Vertical Line !!! The axis of symmetry is halfway in between the two x-intercepts.

8. Axis of Symmetry Your turn: What is the axis of symmetry (the two x-intercepts are given below)? 11. 12. 10.

9. Standard Form: Axis of symmetry: (1) “2 nd ” “calculate” “min/max” “2 nd ” “calculate” “zero” X-value of the vertex tells you the equation of the axis of symmetry. Power of the calculator baby! Graph!

10. Finding the Vertex Open bottom of window further down  y min more negative 2 nd, calculate: Left bound, Right bound, guess Vertex: (3, -17) Axis: x = 3

11. Standard Form: Axis of symmetry: X-value of the vertex tells you the equation of the axis of symmetry. Power of the calculator baby! Graph!

12. Standard Form: Intercept Form: Your turn: 13. Find the vertex of the following parabola: 14. Does the following function have a minimum or a maximum? 15. What is the minimum/maximum value of the following function?

13. Vocabulary Intercept Form: Opens up if positive ‘x-intercepts are: ‘p’ and ‘q’ ‘x-intercepts are: ‘+1’ and ‘+3’ ‘x-intercepts are: ‘-2’ and ‘-4’ Opensdown

14. Your turn: What are the solutions to the following equations? 16. 17. 18.

15. Solve by graphing: Move the “cursor” on the graph to the left of the graph to the left of the left x-intercept. left x-intercept. Move the “cursor” to the right side of the left x-intercept. side of the left x-intercept. Find the left “x-intercept” by hitting: “2 nd ” + “calculate” + “2” (“zero”) “2 nd ” + “calculate” + “2” (“zero”)

16. 19. Solve the quadratic by graphing. 20. Solve the quadratic by graphing.

17. Vocabulary Trinomial: expression with three unlike terms. The sum of 3 unlike monomials Or the product of 2 binomials. Intercept form is the product of 2 binomials!!

18. Smiley Face I call this method the “smiley face”. (x – 4)(x + 2) = ? Left-most term  left “eyebrow” right-most term  right “eyebrow” “nose and mouth” combine to form the middle term. You have learned it as FOIL.

19. Your turn: Multiply the following binomials: 21. 22.

20. Factoring Quadratic expressions: (x + _)(x + _) (_ + _)(_ + _) Multiplied = -5 added = -4 (x + 1)(x – 5)

21. Your Turn: Factor: 23.24.

22. 25. Solve the quadratic by factoring.

23. Do you remember how to solve the quadratic by “extracting a square root”? Isolate the power, undo the power.

24. 27. Solve the quadratic.

25. How many solutions?

26. Remember this? Let’s learn the easy way to do this.

27. Your turn: 28. Simplify 29. Simplify

28. Vocabulary Quadratic Formula: gives the solutions (x-intercepts) to ANY quadratic equation in standard form. a = ? b = ? c = ? a = ? b = ? c = ? This formula is on your reference sheet.

29. The Descriminant is the radicand of the quadratic formula. Two real roots Parabola intersects the x-axis at 2 places one real root Parabola intersects the the x-axis at 1 place The original equation was a perfect square trinomial no real roots Parabola does not intersect the x-axis

30. What if you can’t remember what the Radicand is? “Find the radicand then give the number of type of the solutions for the quadratic equation.” a. 36, two real b. -39, one real c. -36, two imaginary

31. The height (feet) of a falling object on earth can be modeled with the equation 30. When will it hit the ground (h = 0) 31. When will it reach its maximum height? (h is a max)

32. Can’t figure it out?  try graphing Find the equation of a parabola that has x-intercepts of 4 and 1 and passes through the point (3, -4). a.b.c. d. These 3 points are on the parabola: (4, 0), (1, 0), and (3, -4)

33. Your turn: 32. Find the equation Vertex: (3, -1) Point: (x, y) = (2, -4) a. b. c. d.