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

Answer:

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

Step-by-step 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