Which graph represents the function
𝑦 equals negative 0.5𝑥 squared plus four?
We have four different choices
here: a, b, c, or d. First, let’s look at what we know
immediately about our parabola, based on its function. This function has a negative
leading coefficient. Because that leading coefficient is
negative, we know that our parabola will open downward.
The graph in graph a opens upward;
we know that this graph doesn’t represent our function. Graph b also opens upward, and
therefore we know it cannot represent our function. Graph c opens downward; that’s a
possibility. Graph d also opens downward. So we’ve eliminated it to graph c
But there’s something else we can
notice about our function. Our function has a 𝑦-intercept,
and the 𝑦-intercept is positive four. This is the place where this
function crosses the 𝑦-axis. If we put the point zero, four as
the 𝑦-intercept, only one of the functions represents that the 𝑦-intercept of
function d is at negative four.
It cannot represent the function we
were given because the function we were given has a 𝑦-intercept of positive
four. Through process of elimination, we
were able to determine that graph c best represents the function 𝑦 equals negative
0.5𝑥 squared plus four.