Integrated Math 1 B (IS89S) \#90179 | Checkpoint 5 The graph is now opening upward. The graph is now narrower. The graph has now moved down the $$ y $$-axis. The graph now has a new axis of symmetry. The equation $$ y=-6 x^{2}-3 $$ can be graphed in the coordinate plane. Changing the equation to $$ y=-6 x^{2}-5 $$ makes which statement true? Ther

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To analyze the effect of changing the equation from $$ y = -6x^2 - 3 $$ to $$ y = -6x^2 - 5 $$, let's break down the changes step by step:

1. **Original Equation**: $$ y = -6x^2 - 3 $$
   - This is a downward-opening parabola (since the coefficient of $$ x^2 $$ is negative).
   - The vertex of this parabola is at the point $$ (0, -3) $$.

2. **New Equation**: $$ y = -6x^2 - 5 $$
   - This is also a downward-opening parabola.
   - The vertex of this parabola is at the point $$ (0, -5) $$.

### Changes Observed:
- **Direction of Opening**: The direction of opening remains downward for both equations.
- **Width of the Parabola**: The width remains the same since the coefficient of $$ x^2 $$ is unchanged.
- **Vertical Shift**: The graph has moved down the $$ y $$-axis from $$ -3 $$ to $$ -5 $$. This indicates a vertical shift downward.
- **Axis of Symmetry**: The axis of symmetry remains the same, which is the line $$ x = 0 $$ for both equations.

### Conclusion:
The statement that is true after changing the equation to $$ y = -6x^2 - 5 $$ is:
- **The graph has now moved down the $$ y $$-axis.**

This is the correct interpretation of the change in the equation.
The graph has moved down the $$ y $$-axis.

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