Describe how the graph of the function y=x^2 compares to the graph of y= -5/2 x^2

Answer 1

Hello Mary,

Both of these functions are quadratic functions of the form y=ax^2, where a is a non-zero real number. The graph of y=ax^2 is a parabola (u-shaped graph) with vertex at the origin (0,0). However, when a>0 (i.e. positive) the graph opens upward and when a<0 (i.e. negative) the graph opens downward. Hence the graph of y=x^2 is a parabola opening upward with vertex at the origin; and the graph of y=(-5/2)x^2 is a parabola opening downward with vertex at the origin.

Answer 2

y = x^2 is a parabola that opens up as it's a-value (coefficient in front of x^2 term) is positive. -5/2 x^2 is also a parabola but will open downward because a < 0 and it will be a vertical stretch by a scale factor of 5/2.

Answer 3

Both are parabolas going through the origin. The negative flips it and the 5/2's squeezes it such that it grows more negative faster.