Step by step explainations on how to graaph a parabola using a table of values.

Sure! Here is a step-by-step explanation on how to graph a parabola using a table of values:

Step 1: Determine the form of the quadratic equation
Before graphing a parabola using a table of values, it is important to know the form of the quadratic equation. The standard form of a quadratic equation is y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.

Step 2: Choose values for x
Choose a set of values for x to generate corresponding y-values. Select both positive and negative values to get a sense of how the parabola curves.

Step 3: Calculate the corresponding y-values
Using the chosen values for x, substitute them into the equation y = ax^2 + bx + c to find the corresponding y-values. Calculate each y-value by simply plugging the x-value into the equation and simplifying.

Step 4: Create a table of values
Create a table with two columns, one for x-values and the other for their corresponding y-values. List the x-values from step 2 in the first column and the corresponding y-values from step 3 in the second column.

Step 5: Plot the points on a graph
Take the values from the table and plot them on a graph. Use the x-values as the x-coordinates and the corresponding y-values as the y-coordinates. Label each point with its respective coordinates.

Step 6: Draw a curve through the points
Connect the plotted points with a smooth curve. Make sure the curve is symmetric and follows the general shape of a parabola.

Step 7: Add the vertex
Locate the vertex of the parabola on the graph. The x-coordinate of the vertex is given by x = -b / (2a). Substitute this value into the quadratic equation to find the corresponding y-coordinate. Mark the vertex on the graph.

Step 8: Label the axis of symmetry
The axis of symmetry is a vertical line that passes through the vertex. Draw a dashed line representing the axis of symmetry. Label it as "x =" followed by the x-coordinate of the vertex.

Step 9: Find the y-intercept
To find the y-intercept, substitute x = 0 into the quadratic equation and solve for y. The resulting value is the y-coordinate of the point where the parabola crosses the y-axis. Mark this point on the graph.

Step 10: Add any additional features
Depending on the form of the quadratic equation, there may be additional features to consider such as the focus, directrix, or intercepts. You may need additional steps or formulas to calculate and plot these features on the graph.

That's it! By following these steps, you can graph a parabola using a table of values.