Google Earth Engine: Flatten a one-band ImageCollection into a multi-band single Image - google-earth-engine

Question

I want to use supervised classification to classify a pattern that has a clear temporal pattern. For example, identifying stands of deciduous trees in a coniferous forest. NDVI would change overtime in the deciduous stands in a regular pattern that should be easily detectable. I assume there's an easy method to flatten the temporal dataset into a single image so that the bands in that image can be used in a classification algorithm. Maybe using .map(....)?
Here's some code to build the answer from:
var startDate = '2016-05-01';
var endDate = '2016-09-01';
var lng = -122.3424; var lat = 37.9344; //SF
var region = ee.Geometry.Point(lng, lat);
//Image Import
var l8 = ee.ImageCollection('LANDSAT/LC08/C01/T1_TOA')
.filterBounds(region)
.filterDate(startDate,endDate);
// NDVI temporal
var ndvi = l8.map(function(image) {
var ndvi = image.normalizedDifference(['B5', 'B4']).rename("NDVI");
return ndvi;
});
Map.addLayer(ndvi,{},"NDVI Temporal"); // 8 images with 1 band
//NDVI FLATTENED??????? I want 1 image with 8 bands. The below code doesn't work...
var ndviFlat = ee.Image().addBands(ndvi.map(function(image){
var temp = image.select("NDVI");
return temp;
}));
From there, I will pass ndviFlat to .sampleRegions, which only works with Images not ImageCollections:
//Classification Model:
var points = ee.FeatureCollection([trainingPointsPos,trainingPointsNeg]).flatten();
var training = ndviFlat.sampleRegions({
collection: points,
properties: ['class'],
scale: 30
});
var trained = ee.Classifier.randomForest(20).train(training, 'class', bands);
classified = regLayers.select(bands).classify(trained);

Answer 1

Here's one way:
var startDate = '2016-05-01';
var endDate = '2016-09-01';
var lng = -122.3424;
var lat = 37.9344; //SF
var region = ee.Geometry.Point(lng, lat);
//Image Import
var l8 = ee.ImageCollection('LANDSAT/LC08/C01/T1_TOA')
.filterBounds(region)
.filterDate(startDate, endDate);
var empty = ee.Image();
// NDVI temporal
var ndvi = ee.Image(l8.iterate(function(image, previous) {
var name = ee.String('NDVI_').cat(image.id());
var ndvi = image.normalizedDifference(['B5', 'B4']).rename(name);
return ee.Image(previous).addBands(ndvi);
}, empty));
// Remove the annoying non-band
ndvi = ndvi.select(ndvi.bandNames().remove('constant'));
Map.centerObject(region, 13);
Map.addLayer(ndvi, {}, 'ndvi');