A. Solve the quadratic equations. If an equation has no real roots, state this. In cases where the solutions involve radicals, give both the radical form o f the answer and a calculator approximation rounded to two decimal places.

1. x² + 4x + 1 = 0

2. 3y² - 3y - 4 = 0

3. t² = -3t + 4

B.

You are given an equation o fthe form y = ax2 + bx + c. (a) Use a graphing utility to graph the equation and to estimate the x-intercepts. (Use a zoom- in process to obtain the estimates; keep zooming in until the first three decimal places 0 f the estimate remain the same as you progress to the next step.) (b) Determine the exact values 0 f the intercepts by using the quadratic formula. Then use a calculator to evaluate the expressions that you obtain. Round off the results to four decimal places. [ Check to see that your results are consistent with the estimates in part (a).] y= 2x2 + 2J26x +13 ::|-+1s|n| 2 .' lore; B I L! '5 3": XalLli' -'|I|Source The chart that follows shows the world records for the men's 10,000 meter run in the years Time (minutes Year and seconds) Runner 1972 and 1998. 1972 27:38.4 Lasse Viren (Finland) 1998 26:22.75 Haile Gebrselassie (Ethiopia) For the years between 1972 and 1998, the world record can be approximated by the equation y = -0.09781tz + 385.83361 - 378,850.4046 (1972 Source