Multiple Choice
State the vertex, axis of symmetry, and domain & range for each quadratic.
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10. 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:
Verified step by step guidance1
Identify the quadratic function given: \(G(x) = 3(x - 6)^2\). This is in vertex form, which is \(a(x - h)^2 + k\), where \((h, k)\) is the vertex.
Find the vertex by comparing \(G(x) = 3(x - 6)^2\) to the vertex form. Here, \(h = 6\) and \(k = 0\), so the vertex is at \((6, 0)\).
Determine the \(x\)-intercept(s) by setting \(G(x) = 0\) and solving for \(x\): \$0 = 3(x - 6)^2\(. This implies \)(x - 6)^2 = 0\(, so \)x = 6\(. The \)x\(-intercept is \)(6, 0)$.
Find the \(y\)-intercept by evaluating \(G(0)\): \(G(0) = 3(0 - 6)^2 = 3 imes 36\). Calculate this value to get the \(y\)-intercept point \((0, y)\).
State the domain and range: The domain of any quadratic function is all real numbers, so \((-\infty, \infty)\). Since the parabola opens upwards (because \(a=3 > 0\)) and the vertex is the minimum point at \(y=0\), the range is \([0, \infty)\).
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