graph

Graphing the equation $y = 1 + 2x^2$ involves plotting points on a coordinate plane that satisfy the equation. To achieve this, follow these steps:

1. Create a table of values by assigning different values to $x$ and calculating the corresponding $y$ values using the equation.
2. Plot these points on the coordinate plane, with $x$ values on the horizontal axis and $y$ values on the vertical axis.
3. Connect the plotted points with a smooth curve to visualize the graph of $y = 1 + 2x^2$.

This parabola opens upward because the coefficient of the squared term, $2$, is positive. Its vertex, the point where the parabola changes direction, can be found using the formula $x = -\frac{b}{2a}$, which gives $x = 0$ in this case. Plugging this value back into the equation yields $y = 1$, so the vertex is at the point $(0, 1)$.

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Graphing is a mathematical tool used to represent data visually. It allows us to see the relationship between two or more variables and identify patterns or trends. One common type of graph is the linear graph, which is used to plot data points that have a linear relationship. The equation for a linear graph is y = mx + b, where m is the slope and b is the y-intercept.

In the case of the equation y = 5, the slope is 0 and the y-intercept is 5. This means that the graph of this equation will be a horizontal line that passes through the point (0, 5). Horizontal lines are often used to represent constants, which are values that do not change. In this case, the constant is 5.

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Graphing linear equations is a fundamental skill in mathematics. The equation y = 1/2x represents a line that passes through the origin and has a slope of 1/2. To graph this line, follow these steps:

1. Plot the y-intercept. The y-intercept is the point where the line crosses the y-axis. For the equation y = 1/2x, the y-intercept is (0, 0).

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