Question
Which equation has a vertex of (-4,5)
A: y = (x - 4)^2 + 5
B: y = (x+4)^2 - 5
C: y = (x+4)^2 + 5
D: y = (x-4)^2 - 5
A: y = (x - 4)^2 + 5
B: y = (x+4)^2 - 5
C: y = (x+4)^2 + 5
D: y = (x-4)^2 - 5
Answers
GPT-4o mini
To determine which equation has a vertex of (-4, 5), we need to evaluate the vertex form of a quadratic equation, which is given as:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
Given that we are looking for a vertex of (-4, 5), we have:
- \(h = -4\)
- \(k = 5\)
So the equation should be in the form:
\[ y = a(x + 4)^2 + 5 \]
Now let's evaluate the options:
A: \( y = (x - 4)^2 + 5 \)
- Vertex: (4, 5) (not correct)
B: \( y = (x + 4)^2 - 5 \)
- Vertex: (-4, -5) (not correct)
C: \( y = (x + 4)^2 + 5 \)
- Vertex: (-4, 5) (correct)
D: \( y = (x - 4)^2 - 5 \)
- Vertex: (4, -5) (not correct)
The correct choice is **C: y = (x + 4)^2 + 5**.
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
Given that we are looking for a vertex of (-4, 5), we have:
- \(h = -4\)
- \(k = 5\)
So the equation should be in the form:
\[ y = a(x + 4)^2 + 5 \]
Now let's evaluate the options:
A: \( y = (x - 4)^2 + 5 \)
- Vertex: (4, 5) (not correct)
B: \( y = (x + 4)^2 - 5 \)
- Vertex: (-4, -5) (not correct)
C: \( y = (x + 4)^2 + 5 \)
- Vertex: (-4, 5) (correct)
D: \( y = (x - 4)^2 - 5 \)
- Vertex: (4, -5) (not correct)
The correct choice is **C: y = (x + 4)^2 + 5**.