SOLUTION: how can i find the x-intercepts of the parabola with vertex (-1,2) and y-intercept (0,-3)
Algebra.Com
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) (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:
^2\ +\ b(0)\ +\ c\ =\ -3)
^2\ +\ b(-1)\ +\ c\ =\ 2)
^2\ +\ b(-2)\ +\ c\ =\ -3)
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:
\ \pm\ \sqrt{(-10)^2\ -\ 4(-5)(-3)}}{2(-5)} )
Therefore the 
-intercepts are:
\ \approx\ \left(-1.632,0\right))
and
\ \approx\ \left(-0.368,0\right))
John
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