The quadratic expression $21+12x-4x^2$ takes -
- The least value $5$
- The greatest value $30$
- The greatest value $21$
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None of these
Reveal answer
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B
Correct answer
Explanation
The quadratic expression -4x^2 + 12x + 21 has a negative coefficient for x^2, meaning it opens downwards and has a maximum value. The maximum value occurs at x = -b / (2a) = -12 / (2 * -4) = 1.5. Substituting x = 1.5 into the expression gives -4(1.5)^2 + 12(1.5) + 21 = 30.
AI explanation
The expression is -4x^2 + 12x + 21, where the coefficient of x^2 is negative, meaning it attains a greatest value at its vertex. The vertex occurs at x = -12 / (2 * -4) = 3/2. Substituting x = 3/2 into the expression yields -4(3/2)^2 + 12(3/2) + 21 = -9 + 18 + 21 = 30, which is the greatest value.