Answer:
The equation of the parabola is
[tex]y=0.055x^2[/tex]
Step-by-step explanation:
If we have a parabola, we can write that as
[tex]y=ax^2+bx+c[/tex]
As the vertex is in point (0,0), we have that
[tex]0=a\cdot0^2+b\cdot0+c\\\\c=0[/tex]
As the parabola is also symetrical from the y-axis, we have
[tex]y(x)=y(-x)\\\\ax^2+bx=a(-x)^2+b(-x)\\\\ax^2+bx=ax^2-bx\\\\2bx=0\\\\b=0[/tex]
We result in a equation of the parabola as:
[tex]y=ax^2[/tex]
The separation at the opening of the bowl is 34 cm. This opening represents d=2x in the xy-plane.
If the bowl has a depth of 16 cm, we know that at y=16, the value of x should be 34/2=17.
Then we have a point in the parabola that is (x,y)=(17,16).
We can calculate then the paramater a as:
[tex]y=ax^2\\\\16=a(17)^2=289a\\\\a=16/289=0.055[/tex]
