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The type of a quadratic functions' vertex is determined by the coefficient in front of the $x_{2}$-term. For the function $y=2x_{2}−5x+4$ it is $2,$ positive. This means that the curve looks like a happy mouth, and, thus, it's an absolute minimum.

b

Again, look at the coefficient in front of $x_{2}.$ Here it is $-8$, so negative, which means that the curve has the shape of an sad mouth, which means it has an absolute maximum.

c

In this function, there is no $x_{2}$-term. This is because the function is linear. Linear functions does not have any vertex.

d

In
$y=x_{2}+7$
there is an invisible $1$ in front of the $x_{2}$-term. The term can then be written as $1⋅x_{2}.$ Since $1$ is a positive number, the curve looks like a happy mouth, and then has a **minimum point**.