Consider the quadratic function 𝑓 of 𝑥 equals 𝑥 squared minus one. Does the given quadratic function open upward or downward? Does the given quadratic function have a maximum or minimum value? What is the maximum or minimum value of the given quadratic function?
Recall that the shape of a quadratic function is called a parabola, which is a kind of U shape that can either open upward or downward. The graph of the quadratic function 𝑓 of 𝑥 equals 𝑥 squared minus one, as graphed in this image, opens upward. It’s worth noting here that our quadratic function has been given to us in standard form. That’s the forum 𝑎𝑥 squared plus 𝑏𝑥 plus 𝑐. For a quadratic function in this form, if 𝑎 is greater than zero, the parabola will open upward. In this case, we have an 𝑎 value of one.
It follows from parabolas that open upward that they will have a minimum value. We can see this on the graph. If we look at the minimum point of this graph, it’s located at zero, negative one. The minimum value of the function will be the minimum output, and that’s the line that we’ve sketched here 𝑦 equal to negative one.