Question Video: Matching the Rule of a Quadratic Function with Its Graph Mathematics

Which of the following graphs represents 𝑓(π‘₯) = βˆ’(π‘₯ βˆ’ 1)Β² + 2? [A] Graph (a) [B] Graph (b) [C] Graph (c) [D] Graph (d).


Video Transcript

Which of the following graphs represents 𝑓 of π‘₯ equals negative π‘₯ 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 π‘₯ equals a times π‘₯ minus β„Ž squared plus π‘˜. And in standard form, the π‘˜ 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 π‘˜ position. The two is in the π‘˜ 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 π‘₯ minus π‘₯ minus one squared plus two.

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