Seems like someone answered them, because the red writing is right, but here's the answers with explanation
Step-by-step explanation:
The vertex is the point at which the graph changes direction as we go from left to right.
Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.
Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started rising
Now the answers:
Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so <em>minimum</em>
vertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so <em>minimum</em>
vertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is <em>maximum</em>
Vertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is <em>maximum</em>
vertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is <em>minimum</em>
vertex is (0.5,5) because it was getting big then changed and started getting smaller so <em>maximum</em>
