To graph the function \( y = 2x^2 \), follow these steps:
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Identify the shape: The function \( y = 2x^2 \) is a parabola that opens upwards because the coefficient of \( x^2 \) (which is 2) is positive.
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Find the vertex: The vertex of the parabola is at the origin (0, 0) since there are no linear or constant terms in the equation.
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Determine the axis of symmetry: The axis of symmetry is \( x = 0 \) (the y-axis).
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Calculate some key points: Choose several values for \( x \) to find corresponding \( y \) values:
- \( x = -2 \): \( y = 2(-2)^2 = 8 \)
- \( x = -1 \): \( y = 2(-1)^2 = 2 \)
- \( x = 0 \): \( y = 2(0)^2 = 0 \)
- \( x = 1 \): \( y = 2(1)^2 = 2 \)
- \( x = 2 \): \( y = 2(2)^2 = 8 \)
So the points to plot are: \( (-2, 8) \), \( (-1, 2) \), \( (0, 0) \), \( (1, 2) \), and \( (2, 8) \).
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Plot the points: On a coordinate plane, plot the points found.
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Draw the parabola: Connect the points with a smooth curve to form the parabola.
Description of the Graph
- The vertex is at (0, 0).
- The parabola is symmetric about the y-axis.
- As \( x \) moves away from 0 in both the positive and negative directions, \( y \) increases.
If you plot this on graphing software or a graphing calculator, you will see the characteristic U-shape of the function \( y = 2x^2 \).