again, the graph x^2 + 2 does not intercept the x axis.
when x = 0, y =2. so you can expect that it is above the x-axis,
but also intercepting the y-axis.
to find turning point, you can use dy/dx. at turning point,
dy/dx = o. thus, find the value of x and sub it in the eqn y = x^2
+2 to find the corresponding y-value. if you have not learn
differentiation, you can use the visual method to approach the
question.
For example, y = x^2 +2 implies that a x^2 graph (centre
at the 0,0 coordinate) moved 2 units up along the y-axis. so the
turning point would be from (0,0) to (0,2).
for the next question, -x^2 graph implies that the graph is a
x^2 graph, but reflected across the x-axis. i.e it is a x^2 graph
that looks like you drawn it upside down and below the x-axis.
as the above question, the reflected x^2 graph should also cut
the origin at (0,2). since the eqn given is y= -x^2 -3, this
implies that the whole graph shifted 3 units down along the
y-axis. thus the turning point of the graph is (0, -3).
knowing the property of the graph, i.e the shape of the graph,
you should be able to deduce that the line of symmetry is the
x-coordinate of the turning point, i.e the line of symmetry is
x=0.
How do you know the graph is centred at (0,0)?