SOLUTION: how can i find the x-intercepts of the parabola with vertex (-1,2) and y-intercept (0,-3)

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Question 311070: how can i find the x-intercepts of the parabola with vertex (-1,2) and y-intercept (0,-3)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You need to first write the equation of the parabola. We have a vertex at and a -intercept at . The vertex is at a distance of 1 from the -axis. Therefore, because of symmetry, you will find a point on the parabola with a -coordinate of -3 at a distance of 1 on the other side of the vertex, namely the point .

Now that we have three points, we can go about finding the equation of the parabola.

The general equation of a parabola is:



Substituting the values from our three points we get:







A little arithmetic results in the following system of three linear equations:







Solve the system. First substitute -3 for





Multiply the the second equation just above by :





Add the resulting two equations:



And finally by substitution:



Hence, the desired function is:



Find the roots with the quadratic formula since there are no rational factors:









Therefore the -intercepts are:



and




John