The thing about SEO in 2018 is that Google changes its algorithms more than once a day! Reports say that the company changes its algorithms up to 600 times a year. While the majority of those updates consist of smaller changes, among them is the occasional, major update like Hummingbird or Panda that can really wreak havoc with your traffic and search rankings.
I think for agencies as far as how we appear in organic search ourselves, we are definitely going to need to leverage all 3 of the solutions you talk about and agencies who haven't branded their products/services are going to have to do that and are going to have to also employ branding strategies. In addition, we have to optimize for other search ares like you say in your point #2 and we must look at optimizing existing content for voice search and answers/featured snippets like you say in point #3.
Keyword research and analysis involves three "steps": ensuring the site can be indexed in the search engines, finding the most relevant and popular keywords for the site and its products, and using those keywords on the site in a way that will generate and convert traffic. A follow-on effect of keyword analysis and research is the search perception impact.[13] Search perception impact describes the identified impact of a brand's search results on consumer perception, including title and meta tags, site indexing, and keyword focus. As online searching is often the first step for potential consumers/customers, the search perception impact shapes the brand impression for each individual.
Together is better! For many businesses, the best approach is a mix of both organic and paid search results. The advantage of this approach is that organic rankings give a business credibility and evergreen search results. Paid search (PPC) provides immediate top-of-the-page listings and greater click through rates, i.e., sales, when consumers are ready to purchase.
Organic search (SEO): When you enter a keyword or phrase into a search engine like Google or Yahoo!, the organic results are displayed in the main body of the page.When your prospects search for information about your products and services, you want to rank highly in search engine results. By “optimizing” your site, you can improve your ranking for important search terms and phrases (“keywords”). You can also improve your rank by getting other important sites to link to yours.

Another tip you can use is just reach out to the prior agency and say something like the following: “We realise you were using link networks for our website which has resulted in a Google penalty and loss in business. Can you please remove my website from any link network you have built?”. If the prior agency is decent, they will remove the links from the network.
Many people also search specifically for services within their area. Utilizing keywords such as “wedding photography Atlanta” instead of just “wedding photography” can help you face local competition better. Setting up a Google My Business page is also a tool that will help your business pop up in localized searches. It’s free to set up, and requires a physical address for your business.
However, with a properly created PPC campaign, results can be analyzed and any conversion-related problems can fixed within no time. It shouldn’t be surprising to see massive results from a PPC campaign that’s been running only for a few weeks. When and if you have the budget, getting quick results with PPC is not only possible, it’s completely doable.

Whether it may be on social media or your blog, it’s important to publish evergreen posts that do not contain an expiration date. These posts should be engaging and stand out for your readers to stay intrigued. If you’re having trouble of thinking about what to post, consider content that is educational and fun. Statistics show that users tend to share more positive posts than negative ones.
Search engine optimization consultants expanded their offerings to help businesses learn about and use the advertising opportunities offered by search engines, and new agencies focusing primarily upon marketing and advertising through search engines emerged. The term "search engine marketing" was popularized by Danny Sullivan in 2001[12] to cover the spectrum of activities involved in performing SEO, managing paid listings at the search engines, submitting sites to directories, and developing online marketing strategies for businesses, organizations, and individuals.
Google claims their users click (organic) search results more often than ads, essentially rebutting the research cited above. A 2012 Google study found that 81% of ad impressions and 66% of ad clicks happen when there is no associated organic search result on the first page.[2] Research has shown that searchers may have a bias against ads, unless the ads are relevant to the searcher's need or intent [3]

Because so few ordinary users (38% according to Pew Research Center) realized that many of the highest placed "results" on search engine results pages (SERPs) were ads, the search engine optimization industry began to distinguish between ads and natural results.[citation needed] The perspective among general users was that all results were, in fact, "results." So the qualifier "organic" was invented to distinguish non-ad search results from ads.[citation needed]
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