GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A technician is monitoring the voltage (V) across a circuit component, which can be modeled by the function V(t) = 3t^2 - 12t + 15, where 't' is time in seconds. What is the minimum voltage recorded by the technician?
- A15 volts
- B3 volts
- C12 volts
- D6 volts
Show answer & explanationAnswer & explanation
Correct answer: B. 3 volts
The function V(t) = 3t^2 - 12t + 15 is a quadratic with a positive leading coefficient, meaning its graph is a parabola opening upwards, so it has a minimum. The t-coordinate of the vertex is -(-12)/(2*3) = 12/6 = 2. Substitute t=2 into the function: V(2) = 3(2)^2 - 12(2) + 15 = 3(4) - 24 + 15 = 12 - 24 + 15 = 3.
Why the other options are wrong
- A. This is the y-intercept, not the minimum voltage.
- C. This value is incorrect and does not correspond to the minimum of the function.
- D. This value might arise from calculation errors or misinterpreting the vertex formula.
Quadratic Function Vertex
The vertex of a parabola, which is the graph of a quadratic function, represents the maximum or minimum point of the function.
- For f(x) = ax^2 + bx + c, the x-coordinate of the vertex is -b/(2a).
- If a > 0, the parabola opens upwards, and the vertex is a minimum.
- If a < 0, the parabola opens downwards, and the vertex is a maximum.
Memory trick: Vertex: Peak or valley, where the action is!