This problem is a quadratic one, where our sketches will be more accurate and detailed. Our equation starts off in standard form: f(x) = ax^2 + bx + c. But to make it easier to graph we complete the square to put in parent function form: f(x) = a(x - h)^2 + k. This form allows us to find the vertex(max/min), axis, y-intercept, and two x-intercepts much easier and more efficiently.
2. What do you need to pay special attention to in order to understand?
Be sure to correctly write out your steps along the process. To find your parent function form, you begin to complete the square by subtracting 1 from both sides. Continue completing the square by using (b/2)^2 to get 2(x + 2)^2 = 7. To get the parent function form you subtract 7 and your equation is 2(x + 2)^2 -7. You then find your y-intercept by plugging 0 in for x to get y=1. Vertex is (h,k) so that would be (-2, -7). Please note that the x-coordinate is -2 not 2 because h is the opposite of the equation when graphed. Your axis of symmetry is also x=-2 which divides the parabola perfectly in half and in a perfectly symmetrical fashion. You find your x-intercepts by solving 2(x + 2)^2 = 7 and you will get x= -2 +/- square root of 7/2 which will help the symmetry with the plotting of extra points to make the graph even more accurate.