An architect is designing an A-frame house, which is modeled by \( f(x)=-2|x-14|+28 \), where \( x \) is the horizontal distance from the bottom left comer of the house and \( y \) is the vertical distance from the same corner of the house, both measured in feet. Graph this function.

To graph the function \( f(x) = -2|x-14| + 28 \), start by identifying key points. The vertex of the A-frame occurs at \( x = 14 \), where \( f(14) = 28 \). This point, (14, 28), is the highest point of the roof. When \( x \) is less than 14, the function decreases, and it will be symmetrical about this line. At \( x = 0 \), \( f(0) = -2|0-14| + 28 = -2(14) + 28 = 0 \), giving another point (0, 0). Similarly, at \( x = 28 \), the value of \( f(28) \) will also result in (28, 0). The graph has a V shape opening downward, with the vertex at (14, 28), intersecting the x-axis at (0, 0) and (28, 0). To paint a picture, imagine standing in front of this A-frame house; the peak is directly above you, and as you look outward to either side, the slopes of the roof descend evenly, creating that classic triangle-like silhouette you might see in mountain lodgings! This function models not only the aesthetic of the A-frame house but also serves practical applications in architectural design, where maximizing interior space while maintaining a sturdy structure is essential. A-frames are known for their ability to withstand heavy snowfall due to their steeply sloped roofs. In fact, many vacation homes in snowy regions are designed this way for that very logic!