Acc Math 1 Dec. 5 th

1. Acc Math 1 Dec. 5th • WARM-UP • No new warm-up sheet. Just do these on a piece of notebook paper. • Look at this equation: f(x) = -x2 – 8 • 1. What type of function is this? • 2. What kind of transformations would occur to the parent graph to graph this function?

2. RETURN TESTS and REVIEW

3. Quadratic Equations • Quadratic Equations (Functions) have many uses in technology and engineering and are modeled in many natural events. • How can we describe the nature of quadratic equations and graphs and their solutions?

5. The free fall equation S = at2 + Vot + So. is used by anyone predicting the path of a projectile. During WWII I have read that the warships would actually have a mathematician on board to do the calculations when firing at enemy targets. This equation, and how it is derived is shown at http://www.mathmotivation.com/science/freefall.html I once used this equation to calculate the depth of a canyon - I threw a rock straight out, counted the seconds, and was able to use the simplified version S = 16t2 to calculate the depth. Actually, the "canyon" was the bottom side of a dam on a river - my calculated depth gave me the depth of the lake on the dammed up side. Read more: http://wiki.answers.com/Q/Can_you_give_someexamples_of_real-life_application_of_a_quadratic_function_using_x_or_y#ixzz1fPWCIcHy

6. Free Flight A popular example of a parabola in the real world is the trajectory of a ball in free flight. As you throw a ball, it first goes up and forward, then falls down while continuing to travel forward, thus forming an inverted parabola path. A parabolic motion also occurs when a basketball bounces on a hard floor. Another example is a baseball hit by a batter. Rotating Liquid When liquid is rotated, the forces of gravity meet the centrifugal force, which results in the liquid forming a parabola-like shape. The most common example is when you stir up orange juice in a glass by rotating it round its axis. The juice level rises round the edges while falling slightly in the center of the glass (the axis). Another example of rotating liquids is the whirlpool. Reflector Parabola is also used in satellite dishes and flashlights. In satellite dishes it helps reflect signals that then go to a receiver, which interprets the signals and shows satellite-transmitted channels on your TV. In flashlights, automobile headlights and spotlights, parabolic shape helps reflect light. Read more: Real Life Parabola Examples | eHow.comhttp://www.ehow.com/list_7797263_real-life-parabola-examples.html#ixzz1fPWZtcSj

7. Graphing Quad. Functions pp. 3-4 VOCABULARY • Vertex – the lowest/highest point of the parabola (h, k) • Axis of symmetry – the line that divides the parabola into 2 symmetric halves (x = h) • Minimum/maximum value – at the vertex • Extrema – minimum or maximum (the vertex) • Standard form – f(x) = ax2 + bx + c • Vertex form – f(x) = a(x – h)2 + k

8. Characteristics of Quadratics f(x) = x2 Standard Form: f(x) = ax2 + bx + c Transformations: f(x) = a(x – h)2 + k (vertex form) a – h – k –

9. GRAPHING FROM STANDARD FORM Example 1: Graph y = -x2 + 4x – 3 • Because a ___ 0, the parabola opens _________ • FIND the vertex. • First, calculate the x-coordinate x = • Then find the y-coordinate • The vertex is (___, ___). Plot this point

10. GRAPHING FROM STANDARD FORM Example 1: Graph y = -x2 + 4x – 3 • DRAW the axis of symmetry x = _____ • IDENTIFY the y-intercept c, which is _____. Plot the point (___, ___). Then reflect this point across the axis of symmetry to plot another point (___, ___). • EVALUATE the function for x = 1. Plot the point (___, ___) and its reflection on the graph. • DRAW a parabola through the plotted points.

11. Example Example f(x) = 2x2 – 4x – 6 f(x) = 3x2 – 6x + 1 Vertex: Axis of sym: 2 other points:

12. ASSIGNMENT • Pages 5-6 PROBLEMS 1-19