Find the two points of intersection of the graphs y=x2 and y=x+2.
We know the presence of the quadratic means there must be two solutions for x. We can solve this problem by treating the formulas for the graphs as simultaneous equations. We can substitute in the formula for y into the equation involving the quadratic to eliminate the unknown y so we can solve for x. This yields the equation x+2=x2. We need to rearrange this equation so that all numbers are on one side. This makes solving the equation using the quadratic equation or factoring much easier. This gives us x2-x-2=0. We can now factor out this equation by finding the factors of -2 which add to make -1. This gives (x-2)(x+1)=0. For this equation to be true, x=2 and x=-1. We can now substitute these values of x into either equation to get the corresponding y value. This gives the two points of intersection to be (2,4) and (-1,1).
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