VIEWS: 13 PAGES: 17 POSTED ON: 10/4/2012
Name: Date: Topic: Solving & Graphing Quadratic Functions Warm-Up: Factor 1. 49p2 – 100 2. 6d4 + 4d3 – 6d2 – 4d Solve for x: 3. 2x2 + 13x + 6 Quadratic Function (y = ax 2 + bx + c) Vocabulary: 1. Quadratic Parent Function 2. Parabola = the graph of a quadratic function is a U- shaped curved. 3. Axis of Symmetry – divide the graph into two halves The line of symmetry ALWAYS passes through the vertex. Continue 4. Vertex • Minimum – lowest point of the parabola • Maximum – the highest point of the parabola. y Vertex Maximum x Vertex Minimum y = x2 a = 1, b = 0, c = 0 Minimum point (0,0) Axis of symmetry y=x2 x=0 Finding the Line of Symmetry When a quadratic function is in For example… standard form Find the line of symmetry of y= ax2 + bx + c, y = 3x 2 – 18x + 7 The equation of the line of symmetry is Using the formula… b x x 18 18 3 2a 2 3 6 Thus, the line of symmetry is x = 3. Finding the Vertex We know the line of symmetry y = –2x 2 + 8x –3 always goes through the vertex. STEP 1: Find the line of symmetry Thus, the line of symmetry gives us the x – coordinate of x b 8 8 2 2a 2(2) 4 the vertex. STEP 2: Plug the x – value into the original equation to find the y value. To find the y – coordinate of the vertex, we need to plug the x – y = –2(2)2 + 8(2) –3 value into the original equation. y = –2(4)+ 8(2) –3 y = –8+ 16 –3 y=5 Therefore, the vertex is (2 , 5) A Quadratic Function in Standard Form Let's Graph ONE! Try … y y = 2x 2 – 4x – 1 STEP 1: Find the line of symmetry STEP 2: Find the vertex x STEP 3: Find the y-intercept when x = 0. STEP 4: Find two other points and reflect them across the line of symmetry. Then connect the five points with a smooth curve. A Quadratic Function in Standard Form y y= 2x2 – 4x – 1 x What happen if we change the value of a and c ? y=3x2 y=4x2+3 y=-3x2 y=-4x2-2 Conclusion (y = ax 2+bx+c) When a is positive, the graph concaves downward. When a is negative, the graph concaves upward. When c is positive the graph moves up. When c is negative the graph moves down. Other Methods By factoring By using the quadratic formula b b 4ac 2 x 2a Factoring Example X2 - 2x = 0 Factor in order to y=x2-2x solve the equation (Remember to ask yourself does the function have a GCF. Find the x intercept. Two solutions, x=0 and x=2. Find the Solutions y=x2-4 y=x2+2x-15 y=-x2+5 y=-x2-1 Find the solutions y=-x2+4x-1 Group Work: Page 544 – 545 Group 1: Group 3: Group 5: Group 7: #7, #20 #9, #22 #11, #24 #13, #28 Group 2: Group 4: Group 6: Group 8: #8, #21 #10, #23 #12, #25 #14, #30 Independent Work: Page 538 (8, 10) Page 546 (43) Page 549 (a, b, c) HLA#1: Page 538 (7, 8) Page 544 (2, 3, 4)