T25 - Quadratic Functions
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1 Lesson Objectives T25 - Quadratic Functions (1) Establish a context for Quadratic Relations (2) Features of graphs of Quadratic relations D,R,intercepts, vertex (extrema/max/min), axis of symmetry, direction of opening, increase/decrease IB Math SL1 - Santowski (3) Introduce Forms of Quad. Eqns Standard, Vertex (transformational), intercept 10/13/ /13/ The formula for the height, h in meters, of an object launched into the air as a function of its time in flight, t in seconds, is given by is h(t) = - ½ gt 2 + v o t + h o g represents the acceleration due to gravity which is about 9.8 m/s 2, v o refers to the launch velocity in m/s and h o represents the initial launch height in m. If a projectile has an initial velocity of 34.3 m/s and is launched 2.1 m above the ground, graphically determine: (1) the equation that you will enter into the TI-84 (2) the time at which the projectile reaches the maximum height (3) the maximum height reached by the projectile (4) h(2) (5) h -1 (12) (6) state the domain and range of the relation and explain WHY (7) the x-intercepts and their significance (8) the total time of flight of the projectile 10/13/ /13/ (B) Graphic Analysis of Parabolas For our investigation of quadratic functions, you will need to familiar with the following terms: Domain Range Y-intercepts X-intercepts, roots, zeroes Vertex, maximum, minimum, extrema Direction of opening Axis of symmetry Intervals of increase/decrease Concavity Continuity 10/13/ /13/2009 6
2 Graph the parabola f(x) = -x 2 + 4x + 5 and provide a complete graphical analysis of the parabola. Use 10/13/ /13/ Graph the parabola f(x) = 2x 2 + 8x - 24 and provide a complete graphical analysis of the parabola. Use 10/13/ /13/ between the equation f(x) = ax 2 + bx + c and: The eqn and intervals of inc/dec between the equation f(x) = ax 2 + bx + c and: (0,c) (x = -b/2a) The eqn and intervals of inc/dec (x > -b/2a or x < -b/2a) (-b/2a, f(-b/2a)) (y > f(-b/2a)) or y < f(-b/2a)) (sign of a) (sign of a) 10/13/ /13/
3 Graph the parabola f(x) = 2(x + 3) 2-8 and provide a complete graphical analysis of the parabola. Use 10/13/ /13/ Graph the parabola f(x) = - ½ (x - 5) and provide a complete graphical analysis of the parabola. Use your TI-84 to graph and analyze the parabola to help with intercept(s), X- Intervals of 10/13/ /13/ between the equation f(x) = a(x k) 2 + h and: The eqn and intervals of increase/decrease between the equation f(x) = a(x k) 2 + h and (0,f(0)) = ak 2 + h) (x = k ) The eqn and intervals of increase/decrease (x > k or x < k) (h, f(k) = h) (y > h) or y < h) (sign of a) (sign of a) 10/13/ /13/
4 Graph the parabola f(x) = - ½(x + 4)(x 2) and provide a complete graphical analysis of the parabola. Use your TI-84 to graph and analyze the parabola to help with intercept(s), X- Intervals of 10/13/ /13/ Graph the parabola f(x) = 3(x ½ )(x + 3.5) and provide a complete graphical analysis of the parabola. Use your TI-84 to graph and analyze the parabola to help with intercept(s), X- Intervals of 10/13/ /13/ between the equation f(x) = a(x r 1 )(x r 2 ) and: The equation and the roots/zeroes The eqn and intervals of increase/decrease between the equation f(x) = a(x r 1 )(x r 2 ) and: (0,f(0)) = ar 1 r 2 ) The equation and the roots/zeroes (r 1,0) and (r 2,0) x = ½ (r 1 +r 2 ) The eqn and intervals of inc/dec x < ½ (r 1 +r 2 ) or x > ½ (r 1 +r 2 ) (½ (r 1 +r 2 ),f(½ (r 1 +r 2 ))) y > or y < f(½ (r 1 +r 2 )) sign of a sign of a 10/13/ /13/
5 (D) Switching Forms of the Quadratic Equations (1) Write the equation f(x) = 2(x + 3) 2-8 in (2) Write the equation f(x) = - ½ (x - 5) in (3) Write the equation f(x) = 2(x + 3) 2-8 in factored form (4) Write the equation f(x) = - ½ (x - 5) in factored form (D) Switching Forms of the Quadratic Equations (1) Write the equation f(x) = - ½(x + 4)(x 2) in (2) Write the equation 3(x ½ )(x + 3.5) in (3) Write the equation f(x) = - ½(x + 4)(x 2) in vertex form (4) Write the equation 3(x ½ )(x + 3.5) in vertex form 10/13/ /13/ (E) Homework HW: Ex8B.1 #2, Ex 8B.2 #2, 3bf, 6; Ex 8J, #1af, 2acgh, 3bc, 4ad; Ex 8H #3cd, 4acei, 5chk, 6gh IB Packet #4, 5 10/13/
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