Questions: Graph the function: f(x) = 3x² Plot five points on the graph of the function, one point with x = 0, two points with negative x-values, and two points with positive x-values. Then click on the graph to plot these points.

Graph the function: f(x) = 3x² Plot five points on the graph of the function, one point with x = 0, two points with negative x-values, and two points with positive x-values. Then click on the graph to plot these points.
Transcript text: Graph the function: f(x) = 3x² Plot five points on the graph of the function, one point with x = 0, two points with negative x-values, and two points with positive x-values. Then click on the graph to plot these points.
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Solution

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Solution Steps

Step 1: Understand the Function

The given function is \( f(x) = 3x^2 - 2 \). This is a quadratic function, which means its graph will be a parabola.

Step 2: Identify Key Points

To plot the graph, we need to find five points: one point with \( x = 0 \), two points with negative \( x \)-values, and two points with positive \( x \)-values.

Step 3: Calculate the Points

  1. For \( x = 0 \): \[ f(0) = 3(0)^2 - 2 = -2 \] Point: (0, -2)

  2. For \( x = -1 \): \[ f(-1) = 3(-1)^2 - 2 = 3 - 2 = 1 \] Point: (-1, 1)

  3. For \( x = -2 \): \[ f(-2) = 3(-2)^2 - 2 = 3(4) - 2 = 12 - 2 = 10 \] Point: (-2, 10)

  4. For \( x = 1 \): \[ f(1) = 3(1)^2 - 2 = 3 - 2 = 1 \] Point: (1, 1)

  5. For \( x = 2 \): \[ f(2) = 3(2)^2 - 2 = 3(4) - 2 = 12 - 2 = 10 \] Point: (2, 10)

Step 4: Plot the Points

Plot the points (0, -2), (-1, 1), (-2, 10), (1, 1), and (2, 10) on the graph.

Step 5: Draw the Parabola

Connect the points with a smooth curve to form the parabola.

Final Answer

The graph of the function \( f(x) = 3x^2 - 2 \) is a parabola opening upwards with the vertex at (0, -2). The points (-2, 10), (-1, 1), (0, -2), (1, 1), and (2, 10) are plotted on the graph.

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