This problem represents quadratic equations in standard form. This representation includes the detailed explanation of the steps included in order to identify the x-intercepts, y-intercepts, vertex
(max/min), axis of quadratics and how to graph them. We start by completing the square of the a standard form equation so we can then put in in the parent function form [f(x)= a(x-h)^2 + k]. Next, we will graph the equation by locating the vertex, the y-intercept, and up to two x-intercepts, as well as one dotted line, which will be the axis. This will result in an accurate representation of the function.
Of course, there will be many aspects to this equation and you must make sure you notice the characteristics that must be included. For example, you must remember to complete the square correctly by first adding 2 and then factoring out the coefficient from "a". Then, you must find the parent function equation by remembering to subtract the 10 so it all equals to y. Also, one of the main points, is to notice that even though the "h" is negative, you have to get its opposite value and that the "k" remains as is. A common mistake that should not be left out is to get a positive and negative square root 5 and not just a positive value. Lastly, always check that there are at least five points in your graph before connecting the parabola's points (unless there's an imaginary x-intercept, which is not the case in this problem.
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