This initial problem is followed by:
a) What is the equation for the line of symmetry for the graph of the function.
(I think I can solve this )

Please explain and show in detail how to break this down in (dummy language)

b) Asks that the function be graphed based on the initial form of y=a(x-h)^2+k
I know how to graph it once I can solve it.) Why do you not have to plot points when using:
y=a(x-h)^2+k
And note how this graph compares to the graph of y=x^2

The detailed solution elaborates on how to graph the parabola by its basic properties, such as, axis of symmetry, vertex, x- and y-intercepts. It also explains the transformation of parabola functions both mathematically and graphically.

... of a parabola and explain its importance to our daily life: The graph of a parabola describes various kinds of every day, real-world objects and events. ...

...Graph: (6) Table of values: Graph: (7) Table of Graph: values: (8) Table of values: Graph: (9) a = -1 - (-3) = 2 and so, 4a = 8 Graph: The parabola is (y - 6 ...

Examples of graphs: line, parabola, hyperbola, exponential. ... Relate the application to the specific graph (line, parabola, hyperbola, exponential). ...

Graphing A Parabola explained in this answer. ... Connect the dots. You're done! This provides explanation of how to graph a parabola, including opening direction. ...

... Next, it is easy to find that the graph intercepts with y-axis at (0, 8). The symmetric point is (6, 8). From the above five points, we can graph the parabola. ...

... I'll give you some values, and you sketch the graph. By the equation, we know it's a parabola that opens up. It has a line of symmetry at x = 5/2. ...

Graph the parabola using the quadratic formula. (2-(-2)^)^ - 5 x 4. ... (If there is more than one solution, separate them with commas.). Graph the parabola: . ...