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State the vertex, axis of symmetry, and domain & range for each quadratic.
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12. Quadratic Equations and Functions
Graphing Quadratic Equations
Multiple Choice
State the vertex, intercepts, and domain & range for each quadratic.
A
Vertex: ; -intercept: ; -intercept: ; Domain: ; Range:
B
Vertex: ; -intercept: ; -intercept: ; Domain: ; Range:
C
Vertex: ; -intercept: ; -intercept: ; Domain: ; Range:
D
Vertex: ; -intercept: ; -intercept: ; Domain: ; Range:
검증된 단계별 안내1
Identify the given quadratic function: \(G(x) = 3(x - 6)^2\). This is in vertex form, \(a(x - h)^2 + k\), where \((h, k)\) is the vertex.
Determine the vertex by comparing: Here, \(h = 6\) and \(k = 0\), so the vertex is at \((6, 0)\).
Find the \(x\)-intercept(s) by setting \(G(x) = 0\) and solving for \(x\):
\(0 = 3(x - 6)^2\)
Divide both sides by 3, then solve \((x - 6)^2 = 0\) to find \(x = 6\). So the \(x\)-intercept is at \((6, 0)\).
Find the \(y\)-intercept by evaluating \(G(0)\):
\(G(0) = 3(0 - 6)^2 = 3(36) = 108\).
So the \(y\)-intercept is at \((0, 108)\).
State the domain and range:
- Domain of any quadratic function is all real numbers, so \((-\infty, \infty)\).
- Since the parabola opens upward (because \(a=3 > 0\)) and the vertex is the minimum point at \(y=0\), the range is \([0, \infty)\).
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