Graphing a Quadratic Function | Summary and Q&A

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November 7, 2011
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Khan Academy
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Graphing a Quadratic Function

TL;DR

Learn how to graph the function f(x) = -3x^2 + 8 by choosing suitable x values and plotting corresponding y values.

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Key Insights

  • 👈 By sampling x values and calculating f(x) values, we can plot points and visualize the graph of a function.
  • 📉 The graph of f(x) = -3x^2 + 8 is a downward-opening parabola due to the negative coefficient of x^2.
  • 📈 The symmetry of the graph, where f(x) = f(-x), arises from squaring the input in the function definition.

Transcript

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Questions & Answers

Q: How do you graph a function like f(x) = -3x^2 + 8?

To graph the function, select different x values, calculate their corresponding f(x) values, and plot the points on a graph. Then connect the points to create a curve.

Q: Why did the video use specific x values like -2, -1, 0, 1, and 2?

The video chose these x values arbitrarily to demonstrate the general shape of the graph. Using integers makes calculations easier, but any other values could be used.

Q: How did the video determine the y values for each x value?

By substituting the chosen x values into the function equation f(x) = -3x^2 + 8, the corresponding f(x) values were calculated.

Q: Why is the graph of f(x) = -3x^2 + 8 a downward-opening parabola?

The negative coefficient of x^2 in the function equation (-3x^2) causes the parabola to open downwards. The positive constant term (8) shifts the graph upward.

Summary & Key Takeaways

  • The video explains how to graph the function f(x) = -3x^2 + 8.

  • By sampling various x values and calculating their corresponding y values, we can plot the points and connect them to create the graph.

  • The graph of f(x) = -3x^2 + 8 is a downward-opening parabola.

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