Consider the graph that represents the following quadratic equation.
y=-1/3(x+2)^2+5
How does the graph open? Show your work.
The graph of the quadratic equation y=-1/3(x+2)^2+5 opens downward because the coefficient of x^2 term is negative (-1/3).
To show this algebraically, we can rewrite the equation in general form:
y = -1/3(x^2 + 4x + 4) + 5
y = -1/3x^2 - 4/3x - 4/3 + 5
y = -1/3x^2 - 4/3x + 11/3
The coefficient of x^2 term is -1/3 which is negative, therefore the graph opens downward.