Quadratic Functions   f(x) = a(x - h)2 + k -- Part 1.7 -- Write a Quadratic Function in Standard Form   f(x) = x2 + 6x + 8
 Solve Step Graph f(x) = x2 + 6x + 8 Complete the square * f(x) = x2 + 6x + 9 - 9 + 8 Take half of 6 and square it f(x) = (x + 3)2 - 1 (x + 3)2 = x2 + 6x + 9 Vertex (-3, -1) Vertex is (h,k) This means the vertex is shifted 3 units left and 1 unit down from the origin. *Check out  completing the square for help with this step. Click here ....   Write a Quadratic Function in Standard Form                                     f(x) = x2 + 4x + 6 [Solution]  Write a Quadratic Function in Standard Form   f(x) = -x2 + 10x - 5
 Solve Step Graph f(x) = -(x2 - 10x) - 5 Factor out the negative sign first f(x) = -(x2 - 10x + 25 - 25) - 5 Now complete the square* inside parenthesis Remove -25 from parenthesis f(x) = -(x2 - 10x + 25) + 25 - 5 Notice sign change f(x) = -(x - 5)2  + 20 (x - 5)2 = x2 - 10x + 25 Vertex (5, 20) Vertex is (h,k) This means the vertex is shifted 5 units right and 20 units up from the origin. *Check out  completing the square for help with this step. Click here ....   Write a Quadratic Function in Standard Form                                 f(x) = -x2 + 8x - 6 [Solution]  Write a Quadratic Function in Standard Form   f(x) = 2x2 - x - 6
 Solve Step Graph Factor out the 2 first  Multiply out to verify  Now complete the square* inside parenthesis To Remove -1/16 from parenthesis, Multiply it by 2. (x - 1/4)2 = x2 - (1/2)x + 1/16 Simplify the constants Vertex (1/4, -49/8) Vertex is (h,k) This means the vertex is shifted 1/4 unit right and -49/8 units down from the origin. This graph was done with my Online Grapher.              Click here .... *Check out  completing the square for help with this step.  Write a Quadratic Function in Standard Form                                  f(x) = 3x2 - x -  4 [Solution]  