Question

What is the vertex of `y=-3x^2-4x+2`?

Answer 1

`(-2/3,10/3)`

Explanation:

The vertex of a quadratic equation can be found through the vertex formula:

`(-b/(2a),f(-b/(2a)))`

The letters represent the coefficients in the standard form of a quadratic equation `ax^2+bx+c`.

Here:
`a=-3`
`b=-4`

Find the `x`-coordinate of the vertex.

`-b/(2a)=-(-4)/(2(-3))=-2/3`

The `y`-coordinate is found by plugging `-2/3` into the original equation.

`-3(-2/3)^2-4(-2/3)+2=-3(4/9)+8/3+2`
`=-4/3+8/3+6/3=10/3`

Thus, the vertex is located at the point `(-2/3,10/3)`.

This can also be found through putting the quadratic into vertex form `y=a(x-h)^2+k` by completing the square.

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

`y=-3(x^2+4/3x+color(blue)(4/9))+2+color(blue)(4/3)`

`y=-3(x+2/3)^2+10/3`

Again, the vertex is located at the point `(-2/3,10/3)`.