How to Graph a Downward-Opening Parabola

TL;DR

To graph the quadratic function f(x) = -3x^2 + 8, create a table of values by substituting different x-values and calculating the corresponding f(x). Plot the points, connect them to form a parabolic curve, and note that this parabola opens downward because the coefficient of x^2 is negative.

Transcript

We are asked to graph the function f of x is equal to negative 3x squared plus 8. So we'll do this by essentially trying out different points for x, and seeing what we get for f of x, and then graphing it. But the first question I have for you is, just looking at this function definition for f of x, what type of graph will this be? Will just be a l... Read More

Key Insights

• 🍉 The function f(x) = -3x^2 + 8 represents a quadratic equation with a negative coefficient for the x^2 term, indicating a downward-opening parabola.
• 👈 Constructing a table of values by evaluating f(x) for different x-values helps in plotting points on the graph.
• 😥 Connecting the plotted points yields a parabolic curve that matches the shape indicated by the equation.
• ☺️ The x-values chosen for the table determine the width of the parabola on the graph.
• 😀 The y-intercept of the parabola is (0, 8), which is the point where the parabolic curve intersects the y-axis.
• 📭 The vertex of the parabola represents the highest or lowest point on the curve, depending on the direction it opens.
• ❓ The vertex of this particular parabola is located at (0, 8).

Questions & Answers

Q: What type of graph does the function f(x) = -3x^2 + 8 represent?

The graph represents a parabola because of the second-degree term (-3x^2) in the equation.

Q: How can you determine the direction in which the parabola opens?

The coefficient of the x^2 term (-3) indicates that the parabola opens downward.

Q: How do you create a table of values for graphing the function?

By selecting various x-values and evaluating f(x) for each, you can create a table that shows the corresponding y-values.

Q: How do you graph the function using the table of values?

Plot the points from the table on the coordinate plane and connect them to form a parabolic curve that matches the shape determined by the equation.

Summary & Key Takeaways

• The given function, f(x) = -3x^2 + 8, represents a parabola that opens downward.

• By plugging in different values of x into the equation, a table of values can be created to plot the points on a graph.

• Connecting the plotted points forms a parabolic curve that matches the shape determined by the equation.