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

1 Answer
Aug 21, 2016

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]}