Question

can I get these questions done, thank you.

Complete the following problems, showing all your working Marks are allocated to your steps, not just the final answer. Factorise and solve the following quadratic equations: (i)x2 2x 15 0 1. 3x2- 20x 7010x-7 (iii) 64 16x20 2. Use the Quadratic Formula to solve: (i)8x2 - 10x + 2 (ii)3x2 -x -4 0 3. For the parabola y- -x2 + 2x + 8, (i)find the y-intercept (ii) find the x-intercepts (ii) determine whether the parabola has a highest or lowest point (iv) find the coordinates of the highest or lowest point (v)sketch the curve indicating the coordinates of the intercepts and the turning point. 4. A missile is fired into the air from a cliff 20 metres above sea level. The trajectory taken by the missile is given by the formula h --t2 + 8t +20 where h is the height of the missile above sea level and t is the time (in seconds) after it was fired. The missile eventually falls into the sea. (a) How many metres above sea level is the missile after: (i) 3 seconds (ii) 6 seconds (i) How high does the missile go before it begins to fall? (ii) For how long is the missile in the air? (b)

Answer 1

(i) x^2 + 2x -15 = 0 x^2 + 5x -3x -15 = 0 x(x + 5) -3(x + 5) = 0 (x -3) (x + 5) = 0 (x -3) (x + 5) = 0 x = 3, -5 (ii) -3x^2 -20x -70 -10x + 7 = 0 i.e. -3x^2 -30x -63 = 0 i.e. -3(x^2 + 7x + 3x + 21) = 0 i.e. -3 (x(x + 7) + 3(x + 7)) = 0 i.e. -3(x + 3) (x + 7) = 0 i.e. x = -3, x = -7 \r\n (iii) 64 -16 x^2 = 0 -16 (x^2 -4) = 0 -16 (x -2) (x + 2) = 0 x = 2, -2 ax^2 + bx +c = 0 x = -b plusminus squareroot 100 -64/16 x = 10 plusminus squareroot 36/16 x = 10 plusminus 6/6 x = 10 + 6/16