Given the parabola y = ax square + BX + C, | a | = 1 / 2, the coordinates of the highest point are (* 1,5 / 2), find the value of a.b.c | Math enthusiast | Mathematical art

Given the parabola y = ax square + BX + C, | a | = 1 / 2, the coordinates of the highest point are (* 1,5 / 2), find the value of a.b.c

-B / 2A = 1, so B = - 2A
(4ac-b ^ 2) / 4A = 5 / 2, substituting B = - 2A, C-A = 5 / 2
|A | = 1 / 2, so when a = 1 / 2, C = 3, B = - 1
When a = - 1 / 2, C = 2, B = 1
To sum up, a = 1 / 2, B = - 1, C = 3 or
a=-1/2,b=1,c=2

The vertex of parabola y = ax quadratic + BX + C is (- 3, - 1), and a + B + C = 9, find the value of ABC

Know from the title
The axis of symmetry is
-b/(2a)=-3,
That is, B = 6A
And substituting x = - 3 into the curve, we get
9a-3b+c=-1
also
a+b+c=9
One by one elimination
a=5/8
b=15/4
c=37/8
therefore
abc=2775/256

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