Given that the vertex coordinates of a parabola are (- 2,1) and pass through points (1, - 2), the analytic formula of the parabola is obtained

Given that the vertex coordinates of a parabola are (- 2,1) and pass through points (1, - 2), the analytic formula of the parabola is obtained

Let the analytic formula of parabola be y = a (x + 2) 2 + 1, substitute the point (1, - 2) to get, - 2 = a (1 + 2) 2 + 1, the solution is a = - 13, so the analytic formula of parabola is y = - 13 (x + 2) 2 + 1. So the answer is y = - 13 (x + 2) 2 + 1

Given that the vertex coordinates of a parabola are (- 1,2) and pass through points (1, - 2), the analytic expression of the parabola is obtained

The vertex coordinates are (- 1,2),
So y = a [x - (- 1)] & sup2; + 2 = a (x + 1) & sup2; + 2
Over (1, - 2)
Then - 2 = 4A + 2
a=-1
So y = - X & sup2; - 2x + 1

Given the vertex coordinates (- 4,0) of a parabola and passing through (1, - 5), the analytic formula of the parabola is obtained

Suppose that the analytic formula of parabola is (vertex formula): y = a (X-H) ^ 2 + K,
Then: y = a (x + 4) ^ 2,
Substitute (1, - 5) to get: - 5 = a (1 + 4) ^ 2,
So a = - 1 / 5,
So the analytical formula of parabola is y = - 1 / 5 (x + 4) ^ 2

It is known that the parabola intersects the X axis at (- 2.0) (- 3.0) two points and intersects the Y axis at (0.6) to find the expression of this function

The solution consists of two points (- 2.0) (- 3.0) where the parabola intersects the x-axis
Let the parabolic equation be y = a (x + 2) (x + 3)
From the intersection of parabola and Y axis at (0.6)
That is, 6 = a (0 + 2) (0 + 3)
That is, a = 1
That is, the parabolic equation is y = (x + 2) (x + 3)
That is y = x ^ 2 + 5x + 6