a) Draw the graph of y = 2x2 - 3x - 5 for -2 otin x otin 4. b) Use the graph to solve 2x2 - 3x - 5 = 0. c) Using a suitable straight line, solve 2x2 - 5x - 3 = 0.

You're on a roll — 22. Graphing and Solving Quadratic Equations a) Draw the graph of y = 2x^2 - 3x - 5 taking the values of x in the interval -2 x 4. Step 1: Create a table of values for y = 2x^2 - 3x - 5 for the given interval. y = 2x^2 - 3x - 5 | x | 2x^2 | -3x | -5 | y | |-----|--------|-------|------|-----| | -2 | 8 | 6 | -5 | 9 | | -1 | 2 | 3 | -5 | 0 | | 0 | 0 | 0 | -5 | -5 | | 1 | 2 | -3 | -5 | -6 | | 2 | 8 | -6 | -5 | -3 | | 3 | 18 | -9 | -5 | 4 | | 4 | 32 | -12 | -5 | 15 | Step 2: Plot the points from the table on the graph paper. Step 3: Draw a smooth curve through the plotted points to represent the graph of y = 2x^2 - 3x - 5. b) Use the graph to solve the equation 2x^2 - 3x - 5 = 0. To solve 2x^2 - 3x - 5 = 0 using the graph, find the x-intercepts of the curve y = 2x^2 - 3x - 5, which are the points where y=0. From the table of values and by observing where the curve crosses the x-axis: The curve crosses the x-axis at x = -1 and x = 2.5. x = -1 or 2.5 c) Using a suitable straight line, solve the equation 2x^2 - 5x - 3 = 0. Step 1: Relate the given equation 2x^2 - 5x - 3 = 0 to the graph equation y = 2x^2 - 3x - 5. Subtract the target equation from the graph equation: (2x^2 - 3x - 5) - (2x^2 - 5x - 3) = y - 0 2x^2 - 3x - 5 - 2x^2 + 5x + 3 = y 2x - 2 = y The suitable straight line to draw is y = 2x - 2. Step 2: Create a table of values for the straight line y = 2x - 2. | x | y = 2x - 2 | |-----|--------------| | -2 | -6 | | 0 | -2 | | 2 | 2 | | 4 | 6 | Step 3: Plot these points and draw the straight line y = 2x - 2 on the same graph as the curve. Step 4: Identify the x-coordinates of the intersection points between the curve y = 2x^2 - 3x - 5 and the straight line y = 2x - 2. These x-coordinates are the solutions to 2x^2 - 5x - 3 = 0. By observing the intersection points on the graph, the line y = 2x - 2 intersects the curve y = 2x^2 - 3x - 5 at approximately x = -0.5 and x = 3. x = -0.5 or 3 Send me the next one 📸