An equivalent equation of    y = (x – 2)2- 9 is 

Question 1Answer

y = x2 - 4x + 5

y = x2 - 4x - 5

y = x2 + 4x – 5

y = x2 + 4x + 5

To find an equivalent equation to \( y = (x - 2)^2 - 9 \), let's first expand the quadratic expression on the right-hand side.

1. Expand \( (x - 2)^2 \):
\[
(x - 2)^2 = x^2 - 4x + 4
\]

2. Subtract 9 from the result:
\[
y = (x^2 - 4x + 4) - 9
\]
\[
y = x^2 - 4x - 5
\]

Thus, the equivalent equation is:

\[
y = x^2 - 4x - 5
\]

**Answer**: \( y = x^2 - 4x - 5 \)

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. How do you factor a quadratic expression like \( x^2 - 4x - 5 \)?
2. What is the vertex form of a quadratic equation?
3. How can you find the vertex of a parabola from its equation?
4. What is the significance of completing the square in algebra?
5. How do the transformations affect the graph of \( y = (x - 2)^2 - 9 \)?

**Tip**: Always double-check your algebraic expansions to avoid simple mistakes that can lead to incorrect results.

An equivalent equation of y = (x - 2)^2 - 9 is y = x^2 - 4x + 5, y = x^2 - 4x - 5, y = x^2 + 4x - 5, y = x^2 + 4x + 5

Learn how to expand and find the equivalent quadratic equation for y = (x - 2)^2 - 9. This guide provides a step-by-step solution, including key algebraic concepts and the expansion of quadratic expressions. Suitable for students in Grades 8-10.

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