
Andy C. answered 11/01/17
Tutor
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(27)
Math/Physics Tutor
Originally from Lowellville... small world;
played in the Warren Junior Military band
and friend of mine went to Harding.
y = C(x - k)^2 + k where (h,k) is the vertex
y = C(x - (-1))^2 + 7
y = C( x +1)^2 + 7
Now for (-3,-5)
-5 = C(-3 +1)^2 + 7
-5 = C(-2)^2 + 7
-5 = C(4) + 7
-12 = 4c
c = -3
The parabola is y = -3(x+1)^2+7
= -3(x^2+2x+1)+7
= -3x^2 - 6x + 4
As a check: (-1,7) --> -3(-1)^2 - 6(-1) + 4 = -3(1) + 6 + 4 = -3 + 6 + 4 = 3 + 4 = 7 <--- yes, it works
(-3,-5) --> -3(-3)^2 -6(-3) + 4 = -3(9) + 18 +4 = -27 + 18 + 4 = -9 + 5 = -5 <--- yes, it works
By symmetry property of parabolas, the point (-3,5) in relation to the vertex (-1,7) is
12 units up and 2 units to the right.
The reflection is then 2 more units to the right and 12 units down from there.....
so (1,-5)
Plugging this in.... -3(1)^2 - 6(1) + 4 = -3(1) - 6(1) + 4 = -3 - 6+4 = -9 +4 = -5 <--- yes it works!!!
The parabola is y = -3(x+1)^2+7
= -3(x^2+2x+1)+7
= -3x^2 - 6x + 4
= -3(x^2+2x+1)+7
= -3x^2 - 6x + 4