This problem is about identifying the four main parts of a quadratic on a graph. These main parts are the x-intercepts, y-intercepts, vertex (max/min), axis of quadratics (and graphing). This example will show you how to change the quadratic to a parent function equation and will also show you how to graph the quadratic in the end. Also, we will be completing the square so hopefully you haven't forgotten how to do that!
In order to understand how to identify the parts and be able to graph this, you must pay special attention to how you complete the square and getting the correct information on the right (the parent function equation, vertex, etc.) in order to accurately graph the quadratic.
The first step you need to do is to add 10 to the other side, cancelling the 10 on the left. You will then have 2x^2+8x=10. Take out a two for your coefficient and complete the square. You will be left with 2(x+2)^2=18. For the parent function equation, just subtract 18 from both sides and you will have your equation: 2(x+2)^2-18. At this point you can find your vertex, which is (-2, -18). Plug 0 into 'x' to solve for the y-intercept. The axis of symmetry will be x=h so x=-2. Afterwards add 18 back on both sides from the parent graph equation and continue to solve for the x-intercepts. Since your answers for the x-intercepts are whole number and does not have a radical or anything, that will be your exact & approximate answer. Also, since there isn't any imaginary number, you will be able to graph this and it will touch the x-axis.
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