Video: Matching a Quadratic Function to Its Graph

Kathryn Kingham

Which graph represents the function 𝑦 = −0.5𝑥² + 4? [A] Graph (a), [B] Graph (b), [C] Graph (c), [D] Graph (d).


Video Transcript

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.

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