If we know the vertex 1, - 2 of quadratic function and pass through point 1. - 2, then the analytic expression is

If we know the vertex 1, - 2 of quadratic function and pass through point 1. - 2, then the analytic expression is

If we know the vertex 1, - 2 of quadratic function and pass through point 1. - 2, then the analytic expression is
y=(x-1)²-2
y=x²-2x-1

The quadratic function passes through the vertex coordinates (1, - 1) of point (2,0),

Let y = a (x-1) ² - 1;
If (2,0) is brought in, there are:
a(2-1)²-1=0;
a=1;
So y = (x-1) &# 178; - 1 = x & # 178; - 2x;
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Given that the image of a quadratic function takes points (1,3) as vertices and passes through points (2,5), the analytic expression of the quadratic function is?

Let the analytic expression of the function be y = a (x-1) ^ 2 + 3
X = 2, y = 5 into the functional equation
5=a(2-1)^2+3
a=2
The analytic formula of the function is y = 2 (x-1) ^ 2 + 3 = 2x ^ 2-4x + 5