How do you draw the graph of y = 2x2 - 3x + 2 for -3 <= x <= 4?

Hey Born, good to see you again. To draw the graph of y = 2x^2 - 3x + 2 for -3 x 4, we first calculate the y-values for various x-values in the given range. Step 1: Calculate y values for x from -3 to 4. The equation is y = 2x^2 - 3x + 2. For x = -3: y = 2(-3)^2 - 3(-3) + 2 = 2(9) + 9 + 2 = 18 + 9 + 2 = 29 For x = -2: y = 2(-2)^2 - 3(-2) + 2 = 2(4) + 6 + 2 = 8 + 6 + 2 = 16 For x = -1: y = 2(-1)^2 - 3(-1) + 2 = 2(1) + 3 + 2 = 2 + 3 + 2 = 7 For x = 0: y = 2(0)^2 - 3(0) + 2 = 0 - 0 + 2 = 2 For x = 1: y = 2(1)^2 - 3(1) + 2 = 2(1) - 3 + 2 = 2 - 3 + 2 = 1 For x = 2: y = 2(2)^2 - 3(2) + 2 = 2(4) - 6 + 2 = 8 - 6 + 2 = 4 For x = 3: y = 2(3)^2 - 3(3) + 2 = 2(9) - 9 + 2 = 18 - 9 + 2 = 11 For x = 4: y = 2(4)^2 - 3(4) + 2 = 2(16) - 12 + 2 = 32 - 12 + 2 = 22 Step 2: Create a table of values. |c|c| x & y \\ -3 & 29 \\ -2 & 16 \\ -1 & 7 \\ 0 & 2 \\ 1 & 1 \\ 2 & 4 \\ 3 & 11 \\ 4 & 22 \\ Step 3: Find the vertex of the parabola. The x-coordinate of the vertex is given by x = -(b)/(2a). For y = 2x^2 - 3x + 2, a=2 and b=-3. x_v = -(-3)/(2(2)) = (3)/(4) = 0.75 Now, substitute x_v = 0.75 into the equation to find y_v: y_v = 2(0.75)^2 - 3(0.75) + 2 = 2(0.5625) - 2.25 + 2 = 1.125 - 2.25 + 2 = 0.875 The vertex is (0.75, 0.875). To draw the graph: 1. Draw a coordinate plane with the x-axis ranging from at least -3 to 4 and the y-axis ranging from at least 0 to 29. 2. Plot the points from the table: (-3, 29), (-2, 16), (-1, 7), (0, 2), (1, 1), (2, 4), (3, 11), (4, 22). 3. Plot the vertex (0.75, 0.875). 4. Since the coefficient of x^2 (which is 2) is positive, the parabola opens upwards. Draw a smooth curve connecting the plotted points, ensuring it passes through the vertex as its lowest point. The table of values and the vertex are: |c|c| x & y \\ -3 & 29 \\ -2 & 16 \\ -1 & 7 \\ 0 & 2 \\ 1 & 1 \\ 2 & 4 \\ 3 & 11 \\ 4 & 22 \\ Vertex: (0.75, 0.875) Send me the next one 📸