Question:medium

Let \(f(x)\) be a quadratic polynomial in x such that \(f(x)≥0\) for all real numbers x.If \(f(2)=0\) and \(f(4)=6\),then \(f(−2)\) is equal to

Updated On: Jan 15, 2026

  • 12

  • 36

  • 24

  • 6

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The Correct Option is C

Solution and Explanation

Given that the quadratic expression is \( \ge 0 \) for all real \( x \), the parabola opens upwards with a minimum value of zero. The expression passes through \( (2, 0) \) and \( (4, 6) \). Since the expression is 0 at \( x = 2 \), this point is the vertex.

The vertex form of a quadratic is \( y = a(x - h)^2 + k \). With vertex \( (2, 0) \), this simplifies to \( y = a(x - 2)^2 \).

To determine \( a \), we use the point \( (4, 6) \): \( 6 = a(4 - 2)^2 = a \cdot 4 \). Thus, \( a = \frac{6}{4} = \frac{3}{2} \).

The quadratic expression is \( y = \frac{3}{2}(x - 2)^2 \).

Evaluating at \( x = -2 \): \( y = \frac{3}{2}(-2 - 2)^2 = \frac{3}{2} \cdot 16 = 24 \).

Final Answer:

The value of the expression at \( x = -2 \) is \( \boxed{24} \).

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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