To find the inflection points on a graph, you need to take the second derivative. Then, set that equal to zero to find the x value(s) of the inflection point(s).
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Lines are infinite and so do not have a highest or lowest point. You need to have a curve to have a possible lowest point.
' -6 ' and ' 6 ' are not points. On a 2-dimensional (flat) graph, you need two coordinates to locate one point. (On a 3-dimensional (solid) graph, you need three coordinates to locate one point. And there's no such thing as a 1-dimensional graph.)
Draw a tangent to the curve at the point where you need the gradient and find the gradient of the line by using gradient = up divided by across
To graph a parabola you must find the axis of symmetry, determine the focal distance and write the focal as a point, and find the directrix. These are all the main points you need to be able to draw a parabola.
When the x coordinate is changed by adding a constant amount this is the same as translating (shifting) the graph of the function f(x) that amount parallel to the x-axis; if the amount is positive the graph is translated to the left, if it is negative it is translated to the right. As (7, -6) is on f(x), then under the translation f(x + 2), the graph is translated to the left (2 x-values), so the point (7-2, -6) which is the point (5, -6) is the corresponding point on the graph to (7, -6).