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sketch the graph of each function. 5) $y=(x + 2)^2 - 2$ 7) $y=(x - 3)^2 - 2$ 3) $y=(x + 3)^2$ find vertex, 1st, a
To solve for the vertex and axis of symmetry (A.S.) of the quadratic function \( y = (x + 2)^2 - 2 \), we use the vertex form of a quadratic function, which is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex and the axis of symmetry is \( x = h \).
Step 1: Identify \( h \) and \( k \) from the given function
The given function is \( y = (x + 2)^2 - 2 \). We can rewrite \( (x + 2) \) as \( (x - (-2)) \), so comparing with the vertex form \( y = a(x - h)^2 + k \):
- \( h = -2 \) (since \( x - h = x - (-2) = x + 2 \))
- \( k = -2 \) (the constant term)
Step 2: Determine the vertex
The vertex \((h, k)\) is \((-2, -2)\) because \( h = -2 \) and \( k = -2 \).
Step 3: Determine the axis of symmetry
The axis of symmetry for a quadratic function in vertex form \( y = a(x - h)^2 + k \) is the vertical line \( x = h \). Since \( h = -2 \), the axis of symmetry is \( x = -2 \).
Final Answers:
- Vertex (V): \((-2, -2)\)
- Axis of Symmetry (A.S.): \( x = -2 \)
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To solve for the vertex and axis of symmetry (A.S.) of the quadratic function \( y = (x + 2)^2 - 2 \), we use the vertex form of a quadratic function, which is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex and the axis of symmetry is \( x = h \).
Step 1: Identify \( h \) and \( k \) from the given function
The given function is \( y = (x + 2)^2 - 2 \). We can rewrite \( (x + 2) \) as \( (x - (-2)) \), so comparing with the vertex form \( y = a(x - h)^2 + k \):
- \( h = -2 \) (since \( x - h = x - (-2) = x + 2 \))
- \( k = -2 \) (the constant term)
Step 2: Determine the vertex
The vertex \((h, k)\) is \((-2, -2)\) because \( h = -2 \) and \( k = -2 \).
Step 3: Determine the axis of symmetry
The axis of symmetry for a quadratic function in vertex form \( y = a(x - h)^2 + k \) is the vertical line \( x = h \). Since \( h = -2 \), the axis of symmetry is \( x = -2 \).
Final Answers:
- Vertex (V): \((-2, -2)\)
- Axis of Symmetry (A.S.): \( x = -2 \)