Calculate the missing y values using the equation y = 2x2 + 5x - 3.

Here's the solution to question 8: 8. (a) Copy and complete the tables of values for the relation y = 2x^2 + 5x - 3. Step 1: Calculate the missing y values using the equation y = 2x^2 + 5x - 3. For x = -3: y = 2(-3)^2 + 5(-3) - 3 = 2(9) - 15 - 3 = 18 - 15 - 3 = 0. For x = -1.5: y = 2(-1.5)^2 + 5(-1.5) - 3 = 2(2.25) - 7.5 - 3 = 4.5 - 7.5 - 3 = -6. For x = -0.5: y = 2(-0.5)^2 + 5(-0.5) - 3 = 2(0.25) - 2.5 - 3 = 0.5 - 2.5 - 3 = -5. For x = 2: y = 2(2)^2 + 5(2) - 3 = 2(4) + 10 - 3 = 8 + 10 - 3 = 15. Step 2: Complete the table with the calculated values. |c|c|c|c|c|c|c|c|c|c|c| x & -4 & -3 & -2 & -1.5 & -1 & -0.5 & 0 & 1 & 2 & 2.5 \\ y & 22 & 0 & 0 & -6 & -6 & -5 & -3 & 4 & 15 & 22 \\ 8. (b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 2 units on the y-axis, draw the graph of y = 2x^2 + 5x - 3, for the interval -5 x 2.5. This part requires drawing a graph on paper using the specified scale and the values from the completed table. 8. (c) Using your graph in (b), find the truth set of: i) 2x^2 + 5x - 3 = 0. This corresponds to the x-intercepts of the graph where y=0. From the table, y=0 when x=-3 and x=-2. The truth set is \-3, -2\. ii) 2x^2 + 6x - 3 = 0. This equation can be rewritten as 2x^2 + 5x - 3 + x = 0, which means y + x = 0, or y = -x. To solve this graphically, you would draw the line y = -x on the same axes as y = 2x^2 + 5x - 3 and find the x-coordinates of their intersection points. Algebraically, we solve 2x^2 + 6x - 3 = 0 using the quadratic formula x = -b ± sqrt(b^2 - 4ac)2a: x = -6 ± sqrt(6^2 - 4(2)(-3))2(2) x = -6 ± sqrt(36 + 24)4 x = -6 ± sqrt(60)4 x = -6 ± 2sqrt(15)4 x = -3 ± sqrt(15)2 Approximating sqrt(15) ≈ 3.873: x_1 = (-3 + 3.873)/(2) = (0.873)/(2) ≈ 0.437 x_2 = (-3 - 3.873)/(2) = (-6.873)/(2) ≈ -3.437 The truth set is approximately \-3.44, 0.44\. 8. (d) The minimum value of the curve. Step 1: Find the x-coordinate of the vertex using the formula x = (-b)/(2a) for the quadratic equation y = ax^2 + bx + c. For y = 2x^2 + 5x - 3, we have a=2 and b=5. x = (-5)/(2(2)) = (-5)/(4) = -1.25 Step 2: Substitute this x-value back into the equation to find the minimum y-value. y = 2(-1.25)^2 + 5(-1.25) - 3 y = 2(1.5625) - 6.25 - 3 y = 3.125 - 6.25 - 3 y = -3.125 - 3 y = -6.125 The minimum value of the curve is -6.125. Send me the next one 📸