Use the formula 𝑦=(𝑥-3)2+3 to find 𝑦 when:𝑎. 𝑥=-2 , 𝑦=  𝑏. 𝑥=-1 , 𝑦=  𝑐. 𝑥=1 , 𝑦=  𝑑. 𝑥=2 , 𝑦=

1. Break Down the Problem

We need to evaluate the function $y = (x - 3)^2 + 3$ for four different values of $x$:

• $x = -2$
• $x = -1$
• $x = 1$
• $x = 2$

2. Relevant Concepts

We will substitute each value of $x$ into the function to compute the corresponding value of $y$.

3. Analysis and Detail

Let's compute $y$ for each $x$:

1. For $x = -2$: $y = (-2 - 3)^2 + 3 = (-5)^2 + 3 = 25 + 3 = 28$

2. For $x = -1$: $y = (-1 - 3)^2 + 3 = (-4)^2 + 3 = 16 + 3 = 19$

3. For $x = 1$: $y = (1 - 3)^2 + 3 = (-2)^2 + 3 = 4 + 3 = 7$

4. For $x = 2$: $y = (2 - 3)^2 + 3 = (-1)^2 + 3 = 1 + 3 = 4$

4. Verify and Summarize

All calculations are verified and yield the following results for each value of $x$:

• When $x = -2$, $y = 28$
• When $x = -1$, $y = 19$
• When $x = 1$, $y = 7$
• When $x = 2$, $y = 4$

Final Answer

• a. $y = 28$ when $x = -2$
• b. $y = 19$ when $x = -1$
• c. $y = 7$ when $x = 1$
• d. $y = 4$ when $x = 2$