Question

The vertex of the parabola below is at the point (3,2) and the point (4,6) is on the parabola. What is the equation of the parabola?

Answer 1

y=4(x-3)^2+2

Explanation:

Hopefully this helps :)

Answer 2

`\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}`

Explanation:

The vertex form of a parabola:

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

(h, k) - vertex

We have the vertex at (3, 2) → h = 3 and k = 2.

Substitute:

`y=a(x-3)^2+2`

The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:

`6=a(4-3)^2+2` subtract 2 from both sides

`6-2=a(1)^2+2-2`

`4=a\to a=4`

Finally:

`y=4(x-3)^2+2` vertex form

use (a - b)² = a² - 2ab + b²

`y=4(x^2-6x+9)+2` use the distributive property

`y=4x^2-24x+36+2`

`y=4x^2-24x+38` standard form