A quartic function with x-intercept at x=-2 (order 2), a turning point at the origin, and as x approaches + infinity and y approaches negative infinity.

Question

A quartic function with x-intercept at x=-2 (order 2), a turning point at the origin, and as x approaches + infinity and y approaches negative infinity.

Answer 1

x-intercept at x=-2 (order 2)

y = (x+2)^2

a turning point at the origin
y = x^2 (x+2)^2

x→+∞ ==> y → -∞
y = -x^2 (x+2)^2

see the graph at
www.wolframalpha.com/input/?i=-x%5E2+%28x%2B2%29%5E2