As shown in the figure, the parabola intersects with the x-axis at the points A (-1, 0), B (3, 0), and with the y-axis at the point C (0, -3), let the vertex of the parabola is D

Substitute the coordinates of points A, B, C into the quadratic function analytic formula to find a = 1 b = -2 c = -3 then the analytic formula is y = x^2-2x-3

Vertex coordinates transverse coordinates -b/2a , (4ac-b^2)/4a D (1,-4)

Existence, P (0,0) A short note: over the D do the perpendicular line of the axis, so as to introduce the foot of the pendant E. Then triangle BOC and triangle CED is isosceles right triangle

by the image axis of symmetry X = 1 D (1,-4) and OC = OB = 3 angle BCD right angle

has the collinear theorem respectively, the sides are: BC = 3 root 2 CD = root 2 BD = 2 root 5 PC = 3PA = 1 AC = root 10

three pairs of strain Ratio is: root number 2 Therefore, it exists.

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