Explanation:
please remember you middle school and high school classes, homework and exams.
here on college level this is just meant as a quick reminder.
so, what exactly don't you understand, please, so that I can provide specific guidance ?
6
the vertex : the turn-around point, where the parabola curve changes its tendency : (-3, 0.5)
axis of symmetry : since the parabola opens downwards, the axis of symmetry (it is like a mirror for one half of the curve to the other half) is a vertical line going right through the vertex : x = -3
y-intercept is the y-value when x = 0 : (0, -4)
x-intercepts are the x-values when y = 0 :
(-4, 0) and (-2, 0)
max or min : there is only one identifiable extreme value, it is at the vertex, of course, and is clearly a maximum :
at x = -3 the max value of the function is 0.5
the optimal value is the y-coordinate of the vertex (the function value between the 2 x-intercepts) : 0.5
4
y = 0.5x + 6 is linear. why ? because the highest exponent of x is 1. that creates a proportional relationship between x and y meaning y only increases with x in a constant manner.
y = 2x² + 5 is quadratic. why ? because the highest exponent of x is 2. this squares things, in other words, it makes them quadratic.
the graph as third item in the list is neither. the functional value gets exponentially bigger, the closer x gets to 0.
this looks like y = -1/x = x^(-1)
the graph as forth item in the list is a parabola again, and as such it is quadratic.