SOLUTION: Find the x-intercepts of the parabola with vertex of (-4,2) and y-intercept (0,-30).

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Question 1056864: Find the x-intercepts of the parabola with vertex of (-4,2) and y-intercept (0,-30).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the form of the parabola =
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
The formula for the x-value of the vertex is:
+x%5Bv%5D+=+-b%2F%282a%29+
The vertex is at: ( -4, 2 )
+-4+=+-b%2F%282a%29+
+4+=+b%2F%282a%29+
+b+=+8a+
-----------------
The parabola goes through ( 0, -30 )
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+-30+=+a%2A0%5E2+%2B+b%2A0+%2B+c+
+c+=+-30+
----------------------------------
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+y+=+a%2Ax%5E2+%2B+8a%2Ax+-+30+
Find +a+ using ( -4, 2 ) the vertex
+2+=+a%2A%28-4%29%5E2+%2B+8a%2A%28-4%29+-+30+
+32+=+16a+-+32a+
+-16a+=+32+
+a+=+-2+
and
+b+=+8a+
+b+=+-16+
-----------------
The equation is:
+y+=+-2x%5E2+-+16x+-+30+
-----------------------------
Does it go through ( -4,2 ) ?
+2+=+-2%2A%28-4%29%5E2+-+16%2A%28-4%29+-+30+
+2+=+-2%2A16+%2B+64+-+30+
+2+=+-32+-30+%2B+64+
+2+=+-62+%2B+64+
+2+=+2+
OK
Does it go through ( 0,-30 )
Yes
-----------------------------
Find x-intercepts ( roots )
+-2x%5E2+-+16x+-+30+=+0+
+x%5E2+%2B+8x+%2B+15+=+0+
+%28+x+%2B+3+%29%2A%28+x+%2B+5+%29+=+0+
+x+=+-3+
+x+=+-5+
The x-intercepts are:
( -3, 0 )
( -5, 0 )
----------------------
Here's the plot:
+graph%28+400%2C+400%2C+-8%2C+4%2C+-10%2C+4%2C+-2x%5E2+-+16x+-+30+%29+