Question

Find the equation of the parabola in vertex form having a vertex of (2,4) and a y-intercept of (0,2)

Answer 1

`\large\boxed{y=-(1)/(2)(x-2)^2+4}`

Explanation:

The vertex form of a parabola:

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

(h, k) - vertex

We have the vertex (2, 4). Substitute:

`y=a(x-2)^2+4`

The y-intercept (0, 2). Put the coordinates of the y-intercept to the equation:

`2=a(0-2)^2+4`

`2=a(-2)^2+4` subtrzct 4 from both sides

`-2=4a` divide both sides by 4

`-(1)/(2)=a\to a=-(1)/(2)`

Finally:

`y=-(1)/(2)(x-2)^2+4`