The image passes through a (- 1,0), B (3,0), and the function has a minimum value of - 8. What is the analytic expression of this quadratic function? | Math enthusiast | Mathematical art

The image passes through a (- 1,0), B (3,0), and the function has a minimum value of - 8. What is the analytic expression of this quadratic function?

Because the image passes through a (- 1,0), B (3,0),
So let the function be
y=a(x+1)(x-3)
y=ax^2-2ax-3a
=a(x^2-2x)-3a
=a(x-1)^2-4a
Because the minimum value of the function is - 8, that is
-4a=-8
a=2
therefore
The analytic expression of this quadratic function is y = 2 (x + 1) (x-3) = 2x ^ 2-4x-6

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