Correct the y-intercept to (0, -6), noting the negative coefficient of x^2, the vertex at (0, -6), and the parabola opening downward. Plot points symmetrically around the vertex and connect them for an accurate graph.
The error the student made when graphing the linear equation y = -x^2 - 6 is that they plotted the y-intercept at (0, 6), but the correct y-intercept should be plotted at (0, -6). This is because the y-intercept is the point where the line crosses the y-axis, and for this equation, that happens at y = -6.
Here are the steps to correct the graph:
Move the y-intercept point down to (0, -6).
Since the equation is in vertex form, the vertex of the parabola is already correctly plotted at (0, -6).
Remember that the coefficient of the x^2 term is negative, so the parabola opens downwards.
From the vertex, move one unit to the right and two units down to plot another point on the parabola.
Continue plotting points to the left and right of the vertex, following the pattern of moving one unit to the right or left and two units up or down.
Once you have enough points plotted, you can connect them with a smooth curve to complete the graph.