Question

What are the coordinates of the vertex of the parabola?

y=3/4x^2−6x+15

Answer 1

The vertex is the point (4,3)

Explanation:

we have

`y=(3)/(4)x^(2)-6x+15`

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`y-15=(3)/(4)x^(2)-6x`

Factor the leading coefficient

`y-15=(3)/(4)(x^(2)-8x)`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`y-15+12=(3)/(4)(x^(2)-8x+16)`

`y-3=(3)/(4)(x^(2)-8x+16)`

Rewrite as perfect squares

`y-3=(3)/(4)(x-4)^(2)`

`y=(3)/(4)(x-4)^(2)+3` ----> equation in vertex form

The vertex is the point (4,3)