# Find the Points of Intersection of a Parabola with a Line

 This is tutorial on finding the points of intersection of a parabola with a line; general solution. Example 1: Find the points of intersection of the parabola with the line given respectively by their equations y = 2 x 2 + 4 x - 3 2y + x = 4 Solution to Example 1: We first solve the linear equation for y as follows: y = - (1 / 2) x + 2 We now substitute y in the equation of the parabola by - (1 / 2) x + 2 as follows - (1 / 2) x + 2 = 2 x 2 + 4 x - 3 We now group like terms 2 x2 + (9 / 2) x - 5 = 0 Solve the above quadratic equation for x to obtain two solutions x = (- 9 - √(241)) / 8 and x = (- 9 + √(241)) / 8 We now substitute the values of x obtained above into the equation y = - (1 / 2) x + 2 to obtain the values for y as follows y = (41 + √(241)) / 16 and y = (41 - √(241)) / 16 The two points of intersection of the two circless are given by ((- 9 - √(241)) / 8 , (41 + √(241)) / 16 ) and ((- 9 + √(241)) / 8 , (41 - √(241)) / 16 ) Approximated as:(-3.06 , 3.53 ) and (0.82 , 1.59) Shown below is the graph of the parabola, the line and the two points of intersection. More links and references related to the above topics. Find Points Of Intersection of Parabola and Line - Calculator. Interactive tutorial on the Equation of a Parabola. Interactive tutorial on how to find the equation of a parabola. Three Points Parabola Calculator.