Which of the following graphs represents 𝑓 of 𝑥 equals negative 𝑥 minus one
squared plus two?
What do we know about graphing quadratic formulas? Well, we know that any negative quadratic
equations will open downward. Graph a— .
Our function that we’re looking at here is written in standard form. It’s given in the form 𝑓 of 𝑥 equals
a times 𝑥 minus ℎ squared plus 𝑘. And in standard form, the 𝑘 will always represent the minimum or
the maximum depending on if your parabola is opening downward or upward.
Because we already know that our parabola opens downward, we also know that it will have a
maximum value. And the maximum value of our parabola will be whatever is in the 𝑘 position. The
two is in the 𝑘 position of standard form for us. So two is the maximum height of our parabola.
Which parabola, b or c, has a maximum height of two? By looking closely at the graph, we recognize
that parabola b has a maximum height of two. The parabola graphed in b is the only one that could
fit this function, 𝑓 of 𝑥 minus 𝑥 minus one squared plus two.