Question
What is the vertex form of the equation graphed below?
curve is at 1,3
(1 point)
Responses
y=−2(x+1)2−3
y is equal to negative 2 times open paren x plus 1 close paren squared minus 3
y=3(x+1)2−3
y is equal to 3 times open paren x plus 1 close paren squared minus 3
y=3(x−1)2+3
y is equal to 3 times open paren x minus 1 close paren squared plus 3
y=−2(x−1)2+3
curve is at 1,3
(1 point)
Responses
y=−2(x+1)2−3
y is equal to negative 2 times open paren x plus 1 close paren squared minus 3
y=3(x+1)2−3
y is equal to 3 times open paren x plus 1 close paren squared minus 3
y=3(x−1)2+3
y is equal to 3 times open paren x minus 1 close paren squared plus 3
y=−2(x−1)2+3
Answers
GPT-4o mini
To determine the correct vertex form of a quadratic equation that has its vertex at the point (1, 3), we use the vertex form of a quadratic equation:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. In this case, the vertex is (1, 3), so \(h = 1\) and \(k = 3\). The equation can be written as:
\[ y = a(x - 1)^2 + 3 \]
Now we need to identify the correct response among the options provided. We have:
1. **y = −2(x + 1)² − 3**
2. **y = 3(x + 1)² − 3**
3. **y = 3(x − 1)² + 3**
4. **y = −2(x − 1)² + 3**
From this, we can see that option 3, **y = 3(x − 1)² + 3**, has the correct vertex (1, 3).
Therefore, the correct answer is:
**y=3(x−1)²+3.**
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. In this case, the vertex is (1, 3), so \(h = 1\) and \(k = 3\). The equation can be written as:
\[ y = a(x - 1)^2 + 3 \]
Now we need to identify the correct response among the options provided. We have:
1. **y = −2(x + 1)² − 3**
2. **y = 3(x + 1)² − 3**
3. **y = 3(x − 1)² + 3**
4. **y = −2(x − 1)² + 3**
From this, we can see that option 3, **y = 3(x − 1)² + 3**, has the correct vertex (1, 3).
Therefore, the correct answer is:
**y=3(x−1)²+3.**