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A parabola is a symmetrical plane curve that forms when a cone intersects with a plane parallel to its side.
Standard form of a quadratic function represent a parabola.
The equation of parabola is [tex]y=-x^{2} +1.69[/tex]
We have to find the formula for the parabola that has x- intercepts [tex](1.3,0)[/tex] and [tex](-1.3,0)[/tex], and y- intercept [tex](0,1.69)[/tex]
So that, the intercept form of the quadratic equation is;
[tex]y=a(x-p)(x-q)[/tex]
where [tex](-1.3,0)=(p,0)[/tex] and [tex](1.3,0)[/tex] is[tex](q,0)[/tex].
Since, with the vertex being at the y axis and the intercepts at the x axis means that the parabola opens down.
So that,
[tex]1.69=a(0+1.3)(0-1.3)\\ \\1.69=-1.69 a\\ \\a=-1[/tex]
Substituting value of a in above equation.
[tex]y=-1(x+1.3)(x-1.3)\\\\y=-1(x^{2}-1.69 )\\\\y=-x^{2} +1.69[/tex]
Hence, the equation of parabola is [tex]y=-x^{2} +1.69[/tex]
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