Question

1. a. Find the coordinates of the vertex of the quadratic y = 2x2 + 3x – 3. b. Find the maximum and minimum values of 2x2 + 3x – 3 for-25x52. C. Find the exact coordinates of the points where y = 2x² + 3x – 3 cuts the coordinate axes. d. Find the values of k for which 2x2 + 3x - 3 = k will have real roots. (8 marks] 2. Use the discriminant to determine the number of intercepts with the x-axis for each of the following: a. y = 2x² + 20x + 50 b. y = 3x2 - 7x + 2 c. y = 4x2 - x +7 [6 marks] 4. 2x2 – 5x – 1 = 0 has roots a and ß. Use the sum and product of the roots to find the value of o? +82. Do not find the values of a and 8. [4 marks) 6. For the equation (2m - 1)x? + (m - 3)x - 2 = 0, find m such that: a. One root is 2; b. The roots are ta; C. The roots are 8 and (8 marks] 7. If 88-) = 1 and (v2)* = 47-1, find x and y. [6 marks) 8. A triangle has sides of length 7cm, 8cm, 9cm. a. Find, without using a calculator, the cosine of the smallest angle of the triangle. b. Hence determine sin 8. C. Show that the triangle has area 125 cm? (6 marks)

I would like to get answers for this homework as soon as possible .

Answer 1

I (a) y = 2x² + 3x-3 - 2 (a x+ 12/24 33 8 xt 23 2 -0.75 0.75 -4.125 2= 11 y = 33 33 8 Hence coordinate of the venter is /(-0.75, -4.125) x=-0.75 (62 is Given quadratic asymmetric about minimum is -4.125 so, Manimum is y(22=8+ 6-3 11 le) at ze=o ay=-3. and y=0 =) 2x2 + 3x-3=0 -3 I Jet24 2 4 -3t 533 -> x = 4 So, coordinate of the points, where it out the coordinate anes are 33 (0, -3), 1-3 + 173,0), 6 -3- ô 4 62 2x² +38-3-k It has real root if Discriminant so so, 32 -8 (-3-K) & 9 + 24 +8% > -33 k > 33 So, it has real you oots 33 for t> 8 :