Can someone point out what I'm doing wrong here?

In Umbraco 10 I have a simple form on a nav bar which calls a controller method and passes in a coupe of parameters to do a search. The search works fine, I then want to open a page to show the results.

form (this seems fine, it calls the controller as expected):

<form id="test" method="post" class="form-group" asp-controller="Search" asp-action="Search">
            <input id="SearchInput" name="SearchInput" type="text" aria-label="Search Input" />
            <input type="hidden" id="RootId" name="RootId" asp-for="@rootId" />
            <button class="btn btn-primary" type="submit">Submit Search</button>
</form> 

Controller method (again, fine - correct search results are returned):

public ActionResult Search(string SearchInput, string RootId)
{
        var searchResults = _searchService.SearchAllSources(SearchInput, Convert.ToInt32(RootId));
        return View("SearchResults", searchResults);  
}

And the basics of the SearchResults page:

@using MySite.Core.Models;
@inherits Umbraco.Cms.Web.Common.Views.UmbracoViewPage<SearchData>;
@using ContentModels = Umbraco.Cms.Web.Common.PublishedModels;

@{
    var m = Model;
    Layout = "_Layout";
}

<h2>Search Results total: @Model.totalResults</h2>

Should the SearchResults page inherit from it's stronly-typed published model - searchResults - rather than the model used for the searchData? If so, how would I pass the results of the search to it?

If I put breakpoints in the SearchResults page I can see the correct results in the line var m = Model, it then fails as it cant bind model SearchData to IPublishedContent