SOLUTION: Find a formula for the quadratic function whose graph has its vertex at (3,8) and its y-intercept at y=2

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Question 1146996: Find a formula for the quadratic function whose graph has its vertex at (3,8) and its y-intercept at y=2
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-3%29%5E2%2B8
%28y-8%29%2F%28x-3%29%5E2=a
substitute for (0,2):
a=%282-8%29%2F%280-3%29%5E2
a=-6%2F9
a=-2%2F3

highlight%28y=-%282%2F3%29%28x-3%29%5E2%2B8%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The location of the vertex is at +-b%2F%282a%29+
when the equation is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
-------------------------------
The vertex is at ( 3, 8 )
+8+=+a%2A3%5E2++%2B+b%2A3+%2B+c+
+8+=+9a+%2B+3b+%2B+c+
-------------------------------
Also:
+3+=+-b%2F%282a%29+
+b+=+-6a+
-------------------------------
The y-intercept is at ( 0, 2 )
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+2+=+a%2A0%5E2+%2B+b%2A0+%2B+c+
+c+=+2+
------------------------------
By substitution:
+8+=+9a+%2B+3b+%2B+c+
+8+=+9a+%2B+3%2A%28-6a%29+%2B+2+
+8+=+9a+-+18a+%2B+2+
+9a+=+-6+
+a+=+-2%2F3+
and
+b+=+-6a+
+b+=+-6%2A%28-2%2F3%29+
+b+=+4+
-----------------------------
The equation is:
+y+=+%28-2%2F3%29%2Ax%5E2+%2B+4x+%2B+2+
------------------------------
check:
( 3,8 )
+8+=+%28-2%2F3%29%2A9+%2B+4%2A3+%2B+2+
+8+=+-6+%2B+12+%2B+2+
+8+=+8+
OK
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Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+10%2C+-5%2C+10%2C+%28-2%2F3%29%2Ax%5E2+%2B+4x+%2B+2+%29+