객관식
Graph the following quadratics and state its vertex and intercepts.
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12. Quadratic Equations and Functions
Graphing Quadratic Equations
Multiple Choice
Graph the following quadratics and state its vertex, intercepts and domain & range.
A
Vertex: ; -intercepts: ; -intercept: ; Domain: ; Range:
B
Vertex: ; -intercepts: ; -intercept: ; Domain: ; Range:
C
Vertex: ; -intercepts: ; -intercept: ; Domain: ; Range:
D
Vertex: ; -intercepts: ; -intercept: ; Domain: ; Range:
검증된 단계별 안내1
Identify the quadratic function given: \(f(x) = -\frac{3}{2}x^2 - 6x + 6\).
Find the vertex using the vertex formula \(x = -\frac{b}{2a}\), where \(a = -\frac{3}{2}\) and \(b = -6\). Substitute \(x\) back into the function to find the \(y\)-coordinate of the vertex.
Calculate the \(x\)-intercepts by setting \(f(x) = 0\) and solving the quadratic equation \(-\frac{3}{2}x^2 - 6x + 6 = 0\) using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Find the \(y\)-intercept by evaluating \(f(0)\), which is the constant term in the quadratic function.
State the domain and range: The domain of any quadratic function is all real numbers \((-\infty, \infty)\). Since the parabola opens downward (because \(a < 0\)), the range is \((-\infty, y_{vertex}]\), where \(y_{vertex}\) is the \(y\)-value of the vertex.
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