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The question is asking about the translation of the graph from the equation \( y = 6x^2 \) to the equation \( y = 6(x + 1)^2 \).

### Step-by-step explanation:

1. The original equation is \( y = 6x^2 \), which is a parabola centered at the origin.
2. The new equation is \( y = 6(x + 1)^2 \). This form represents a horizontal shift of the parabola.
3. In general, for an equation \( y = a(x - h)^2 \), the graph is shifted horizontally by \( h \) units. If \( h \) is positive, the shift is to the right. If \( h \) is negative, the shift is to the left.
4. In \( y = 6(x + 1)^2 \), notice that the expression inside the parentheses is \( (x + 1) \), which is equivalent to \( (x - (-1)) \). This indicates a shift **1 unit to the left**, not to the right.

Thus, the correct translation is **1 unit left**, not right. The correct answer should be the last option, "1 unit left."

Would you like more details, or do you have any questions about this process?

### Related questions:
1. How does a vertical translation affect a parabola's graph?
2. What is the effect of changing the coefficient of \( x^2 \) in a quadratic equation on its graph?
3. Can you describe the effect of a vertical stretch on the parabola \( y = ax^2 \)?
4. What is the general formula for a parabola, and how can you identify shifts from it?
5. How would you identify both horizontal and vertical shifts in a function like \( y = a(x - h)^2 + k \)?

### Tip:
When interpreting shifts in a graph, always check for both horizontal and vertical translations and remember that signs inside parentheses opposite the expected direction.

Which phrase best describes the translation from the graph y = 6x^2 to the graph of y = 6(x + 1)^2?

Understand the horizontal translation of the parabola y = 6x^2 to y = 6(x + 1)^2. This problem involves analyzing the transformation of a quadratic equation's graph, focusing on horizontal shifts. Suitable for students in Grades 9-10.

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