Question

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

Answer 1

Vertex is at the origin `(0,0)`

Explanation:

This is a somewhat unusual format for a parabola! Simplify first to see what we are working with..

`y = x^2 +4x +4 -3x^2 -4x -4 = -2x^2`

What does an equation tell us about the parabola?

The standard form is `y = color(red)(a)x^2 + color(blue)(b)x + color(magenta)(c)`

`color(red)(a)` changes the shape of the parabola - whether it is narrow or wide, or open upwards or downwards.

`color(blue)(b)x` moves the parabola to the left or right

`color(magenta)(c)` gives the y-intercept. It moves the parabola up or down.

In `y = -2x^2` there is no x-term, and `c = 0`

This means that the parabola has not moved to the left or right, nor has it moved up or down, although it is 'upside-down' with a maximum TP.

Its vertex is at the origin `(0,0)`

Changing it to vertex form will give `y =-2(x+0)^2 + 0`
graph{-2x^2 [-4.92, 5.08, -3.86, 1.14]}