Questions: Graph the equation by plotting points. y=2x^2 To graph the equation, plot at least five points. Then click on the graph icon.

Transcript text: Graph the equation by plotting points. \[ y=2 x^{2} \] To graph the equation, plot at least five points. Then click on the graph icon.

Solution

Solution Steps

Step 1: Understand the Equation

The given equation is \( y = 2x^2 \). This is a quadratic equation, which represents a parabola opening upwards.

Step 2: Choose Points to Plot

To graph the equation, we need to choose at least five points. Common choices are \( x = -2, -1, 0, 1, 2 \).

Step 3: Calculate Corresponding y-values

For \( x = -2 \): \[ y = 2(-2)^2 = 2 \cdot 4 = 8 \]
For \( x = -1 \): \[ y = 2(-1)^2 = 2 \cdot 1 = 2 \]
For \( x = 0 \): \[ y = 2(0)^2 = 0 \]
For \( x = 1 \): \[ y = 2(1)^2 = 2 \cdot 1 = 2 \]
For \( x = 2 \): \[ y = 2(2)^2 = 2 \cdot 4 = 8 \]

Step 4: Plot the Points

Plot the points \((-2, 8)\), \((-1, 2)\), \((0, 0)\), \((1, 2)\), and \((2, 8)\) 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 equation \( y = 2x^2 \) is a parabola opening upwards with the vertex at the origin \((0, 0)\). The points \((-2, 8)\), \((-1, 2)\), \((0, 0)\), \((1, 2)\), and \((2, 8)\) should be plotted and connected to form the graph.

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