The equation of the parabola is y = -1/3 ([tex]x^2[/tex]+4x).
What is parabola ?
A bowl-shaped object forms a curve when the surface of the cone intersects a plane perpendicular to a straight line. Another curve is created when the moving point is moved such that the distance from the fixed point is equal to the distance from the fixed line. A parabola is a U-shaped curve representing the graph of a quadratic function. Graph of the equation y=x2,
Here the equation of the parabola is
=> y= a[tex]x^2[/tex]+bx+c.
Now pt given points to find value of a, b, c .
=> y = a(x-p)(x-q)
=> y = a(x+2-2)(x+2+2)
=> y = a(x)(x+4)
Here the line passes through the point ,
(x,y) = (-1,1)
=> 1 = a(-1)(-1+4)
=> 1 = a (-3)
=> a = -1/3.
Now the equation is ,
y = a (x)(x+4)
=> y = -1/3 ([tex]x^2[/tex]+4x)
Therefore the equation of the parabola is y = -1/3 ([tex]x^2[/tex]+4x).
To learn more about parabola refer the below link
https://brainly.com/question/4061870
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