Determine the coordinates of the intersection point(s) between the line y = x^2 + 4x - 8 and y = - 2x - 17
Step 1 - Label y = x2 + 4x – 8 as equation 1 and y = - 2x – 17 as equation 2.Step 2 - In this particular question it is easier to eliminate the y variable from both equations, as they are both are in the form y = _. At the intersection point the y coordinate of the two equations will be the same so let equation 1 = equation 2: x2 + 4x – 8 = - 2x – 17 Step 3 - Rearrange in order to get all the terms on one side of the equation:x2 + 4x – 8 + 2x + 17 = 0Step 4 - Simplify the equation by adding/subtracting like terms: x2 + 6x + 9 = 0Step 5 - Factorise the quadratic: (x + 3)(x + 3) = 0 Step 6 - Determine the solution(s) of this quadratic (i.e. the value(s) of x for which this quadratic is equal to 0) by setting each bracket equal to 0: x + 3 = 0 Therefore, x = - 3 (Note: in this question there is only 1 solution, as both brackets are the same)Step 7 - Find the value of y which equates to this value of x by substituting x = - 3 into equation 2: y = - 2(- 3) – 17 y = 6 – 17 y = - 11Step 8 - Write your answer as a coordinate: (- 3, - 11)Step 9 - Check your answer by substituting x = - 3 into equation 1 to confirm y = - 11: (- 3)2+ 4(- 3) – 8 = 9 – 12 - 8 = - 11
