Digital ACT Math Practice Question #1166
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Consider what \( f(1) \) represents in terms of \( a, b, \) and \( c \).
Recall that the minimum value of a quadratic function occurs at its vertex.
Recognize that \( a+b+c \) is simply the value of the function when \( x=1 \), i.e., \( f(1) \). The problem explicitly states that the minimum value of the function is \( -4 \) and it occurs at \( x=1 \). Therefore, \( f(1) = -4 \). This directly gives the value of \( a+b+c \) without needing to solve for \( a, b, \) or \( c \) individually. This shortcut saves significant time and reduces the chance of algebraic errors.
The problem states that the quadratic function \( f(x) = ax^2 + bx + c \) has a minimum value of \( -4 \) at \( x = 1 \). For a quadratic function, the minimum (or maximum) value occurs at its vertex. Therefore, the vertex of the parabola i...
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