Question

See attachment.

Answer 1

vertex is (-5,3) from your eyeballs, because you have
\[y=\frac{1}{5}(x+5)^2+3\] and the first term will be zero only if x = -5, otherwise it will be positive

Answer 2

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Answer 3

\[(x+5)^2\geq 0\] for any number x, because it is a square. that means the very smallest it can be is 0, and it is 0 when x = -5

Answer 4

ok?

Answer 5

so the very smallest
\[\frac{1}{5}(x+5)^2+3\] can be is 3, and it is 3 if x = -5
that is why the vertex is
\[(-5,3)\]

Answer 6

ok

Answer 7

that means the "axis of symmetry" is
\[x=-5\]

Answer 8

it also means the minimum value of y is 3

Answer 9

ok

Answer 10

and since you have a parabola that opens up, and has vertex at (-5,3) it also means your graph is choice b, which is the only one that satisfies those conditions

Answer 11

Ok. Is it a minimum or maximum value?

Answer 12

look at the picture, and also what i wrote above, and it will be clear whether 3 is the biggest or the smallest that y can be

Answer 13

?

Answer 14

i mean this part