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 or d.
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.