Answer :
Answer:
The equation of parabola in vertex form is [tex]y=0.015(x+0.5)^2+2.3[/tex]
Step-by-step explanation:
Given coordinate of vertex is [tex](-\frac{1}{2},2.3)[/tex] and the parabola passes through the point [tex](5,2\frac{3}{4})[/tex]
So, the equation of parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex]
Where [tex](h,k)[/tex] is the coordinate of the vertex.
[tex](h,k)=(-\frac{1}{2},2.3)=(-0.5,2.3).\\\\So,\ h=-0.5\ and\ k=2.3[/tex]
Plugging these value in equation we get,
[tex]y=a(x-(-0.5))^2+2.3\\\\y=a(x+0.5)^2+2.3[/tex]
Now, we will find the value of [tex]a[/tex]
Plug the coordinate [tex](5,2\frac{3}{4})[/tex]
[tex](x,y)= (5,2\frac{3}{4})\\\\(x,y)=(5,\frac{11}{4})\\\\(x,y)=(5,2.75)[/tex]
[tex]2.75=a(5-(-0.5))^2+2.3\\\\2.75=a(5+(0.5))^2+2.3\\\\2.75=a(5.5)^2+2.3\\\\2.75=a\times30.25+2.3\\\\2.75-2.3=a\times30.25\\\\0.45=a\times30.25\\\\\frac{0.45}{30.25}=a\\ \\a=0.0149[/tex]
Plug the value of [tex]a[/tex] in the equation [tex]y=a(x+0.5)^2+2.3[/tex]
So, the equation of parabola with vertex [tex](-\frac{1}{2},2.3)[/tex] and passes through the point [tex](5,2\frac{3}{4})[/tex] is
[tex]y=0.0149(x+0.5)^2+2.3[/tex] ≅[tex]y=0.015(x+0.5)^2+2.3[/tex]