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A parabola contains points 0,0 , −1,1 and 1,5 . What is the equation of this parabola in standard form? 4-3:MODELING WITH QUADRATIC FUNCTIONS y ax 2 bx c y ax 2 bx c y ax 2 bx c 0 a 0 b 0 c 1 a 1 b 1 c 5 a 1 b 1 c 0c 1 a bc 5 abc 2 2 2 Algebra 2 a b c 1 a b c 5 a b 1 a b 5 a3 b2 y 3x 2 2 x Draw the rectangular number next in the series: Find the next two rectangular numbers: 1 2 1 2 23 3 4 45 5 6 5 6 2 3 4 5 6 7 42 1 6 42 1 2 3 4 5 6 # of Dots Complete the table for the values given and graph the data: Total dots 1 2 2 6 3 12 4 20 5 45 # of Dots # of Dots Term Number 3 4 6 7 Term # Term # 23 30 1) What equation does the graph suggest? A Quadratic (parabola) 78 8 9 56 72 2) Plot the data in your calculator. Press: STAT>EDIT>L1 Enter the data under Term Number. 3) Use the arrow keys to move through to L2. Enter the data you found under Total Dots. 4) Set an appropriate window for the values. 5) View the graph: Does it resemble your hand made graph? The equation is of the form: y ax 2 bx c a= b= c= 1 1 0 Final equation: 2 x x 5) Calculate the equation of the line of best fit: Press: STAT>CALC>#5 QuadReg 6) Choose the Lists that your data is stored under. (Ex. L1, L2) Press: Enter 1 7)Enter the equation of the line under 2 Y= x x 8)Graph the equation. Does it fit the data? Yes, the parabola graphed goes through the points. 9) Use your equation to calculate the 100th term in the series. x 2 x 1002 100 10,100 Homework: p.212 #7-25 odd 2