\f1. Standard form: y=x - Bx + 7 Factored form: x-intercepts: Vertex (show all work): Graph: geyerinstructional.com #150246 X y -1 CD COFinding the vertex using x-intercepts Once you have found the x-intercepts for a quadratic relation, it is possible to find the vertex using the property of symmetry (all parabolas are symmetrical) First, you must find the value of x that is exactly in between your x-intercepts: Ex/ (2,0) and (4,0) Find the average of your x values by adding up your two x-intercepts and then dividing by 2 214 = 3 This gives you the x-coordinate of your vertex. Now you can substitute your x-coordinate back into your equation to find your y-coordinate. (You have the choice to use the equation in either factored form or standard form) y = (x - 2) (x - 4) y = x - 6x + 8 y = (3 - 2)(3 - 4) y = (3) - 6(3) + 8 y = (1)(- 1) y =9 - 18 + 8 y =1 =- 1 Now simply format your answer into a coordinate point: Vertex: (3,-1) Take a look at the graph on the previous page to confirm your answer Now it's your turn! For this assignment you will: change quadratic equations from standard form to factored form use the factored form to find the x-intercepts average the x-intercepts to find the x-coordinate of the vertex substitute the x value back to the equation to find the y-coordinate of the vertex confirm your answers by graphingFinding x-intercepts in factored form What can factoring a quadratic equation tell you? When you factor a quadratic equation, it becomes possible to easily find the x-intercepts of the corresponding graph. Ex/ y = x - 6x + 8 Start by putting this equation into factored form: y = (x - 2)(x - 4) As we know that x-intercepts have 0 as their y-coordinate, we must find two different values of x that will make the whole equation equal to 0. We also know that 0 multiplied by any number makes 0, hence we can look at each set of brackets separately: 0 =x- 2 0=x-4 x=0+2 x=0+4 * =2 x = 4 Lets look at this on a graph: Can you spot the x-intercepts? How about the vertex