Question

Write the equation of the parabola that has the vertex at point (− 1/2 ,2.3) and passes through the point (5,2 3/4 ).

Answer 1

The equation of parabola in vertex form is
`y=0.015(x+0.5)^2+2.3`

Explanation:

Given coordinate of vertex is
`(-(1)/(2),2.3)` and the parabola passes through the point
`(5,2(3)/(4))`

So, the equation of parabola in vertex form is

`y=a(x-h)^2+k`

Where
`(h,k)` is the coordinate of the vertex.

`(h,k)=(-(1)/(2),2.3)=(-0.5,2.3).\\\\So,\ h=-0.5\ and\ k=2.3`

Plugging these value in equation we get,

`y=a(x-(-0.5))^2+2.3\\\\y=a(x+0.5)^2+2.3`

Now, we will find the value of
`a`

Plug the coordinate
`(5,2(3)/(4))`

`(x,y)= (5,2(3)/(4))\\\\(x,y)=(5,(11)/(4))\\\\(x,y)=(5,2.75)`

`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*30.25+2.3\\\\2.75-2.3=a*30.25\\\\0.45=a*30.25\\\\(0.45)/(30.25)=a\\ \\a=0.0149`

Plug the value of
`a` in the equation
`y=a(x+0.5)^2+2.3`

So, the equation of parabola with vertex
`(-(1)/(2),2.3)` and passes through the point
`(5,2(3)/(4))` is

`y=0.0149(x+0.5)^2+2.3` ≅
`y=0.015(x+0.5)^2+2.3`