The soil looks very dry. I am not sure where you are located, I live in south florida and the sun would not be an issue for a foxtail palm (assuming it has been in full sun at the nursery). I would possibly dig up the rootball (be sure not to disturb the roots) and dig a hole twice the size of the the rootball and work in some garden soil (be careful not to use too much). Then I would mulch the area to hold moisture and water regularly until the soil changes. Just and idea :)

When you water, does the water absorb right away or does it just run?

I think it is sunburn too.

I live in the Caribbean, so it is always sunny and hot. The nursery had it in a shady area. I dug a deep hole, put potting soil and then the plant. It was enveloped in the dirt that was in the nursery pot.

The landscaping people put sand on the area around to try to plant grass. I will try to water more. I was depending a lot on the water sprinkler. I think the water dries up when it gets wet.

I bought 2 palms and they are both like that now.

Then it is sunburn.Yes,water alot more.In time the palm will get used to the sun.

You'll be in a similar climate from where Foxtails come, but any plant going from shade suddenly into direct sun will get burned. Those fronds won't recover but they will be replaced. Just takes time..