other graph and modelling

Question

sketch the graph of the following, clearly showing the coordinates of the turning point and the intercepts with the axes. y=2xsquared +3 , y=1/4 - 1/2x squared, y=4(2-x)cubic

Answer 1

y=2x^2+3. This is a parabola with vertex at (0,3), which is the turning point

y=1/4-(1/2)x^2 is also a parabola (inverted U) with vertex and turning point at (0,1/4).

y=4(2-x)^3. When x=2 there is a turning point at (2,0) but it's quite flat.

In the picture below the red curve is y=x^2+3, the blue curve is y=¼-½x^2 and the yellow curve is y=4(2-x)^3.