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Find the vertex and axis of symmetry and determine the direction that the parabola opens.
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12. Conic Sections & Systems of Nonlinear Equations
Parabolas
Multiple Choice
Find the vertex and axis of symmetry and determine the direction that the parabola opens.
A
Parabola opens downwards; Vertex: ; Axis of symmetry:
B
Parabola opens upwards; Vertex: ; Axis of symmetry:
C
Parabola opens upwards; Vertex: ; Axis of symmetry:
D
Parabola opens downwards; Vertex: ; Axis of symmetry:
검증된 단계별 안내1
Identify the given quadratic function in vertex form: \(y=\left(x+4\right)^2 - 9\).
Recall that the vertex form of a parabola is \(y = a(x-h)^2 + k\), where \((h, k)\) is the vertex. Here, rewrite \(x+4\) as \(x - (-4)\) to identify \(h = -4\) and \(k = -9\).
Determine the vertex from the values of \(h\) and \(k\). The vertex is at the point \(\left(-4, -9\right)\).
Find the axis of symmetry, which is the vertical line passing through the vertex. This line is given by \(x = h\), so the axis of symmetry is \(x = -4\).
Determine the direction the parabola opens by looking at the coefficient \(a\) in front of the squared term. Since the squared term is positive (coefficient \(a = 1\)), the parabola opens upwards.
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