Write the equation of the parabola in vertex form with vertex at (2,-5) and y intercept at -17.
1 answer:
<h3>Answer:</h3>
y = -3(x -2)² -5
<h3>Explanation:</h3>The equation of a parabola with vertex (h, k) is given by ...
... y = a(x -h)² +k . . . . . . . for some vertical scale factor "a".
We can find the value of "a" by substituting the coordinates of a point that is not the vertex. Here, that point is the y-intercept: (0, -17).
... y = a(x -2)² -5 . . . . . initial form of the equation for the parabola
... -17 = a(-2)² -5 . . . . . substitute y-intercept values
... -12 = 4a . . . . . . . . . . add 5, simplify
... -12/4 = a = -3
The desired equation is ... y = -3(x -2)² -5.
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Answer:
B) 176 ft²
Step-by-step explanation:
The picture below is the attachment for the complete question. The figure has 3 halves of a circle and a square . The area of the figure is the sum of their area.
Area of a square
area = L²
where
L = length
L = 9 ft
area = 9²
area = 81 ft²
Area of the 3 semi circles
area of a single semi circle = πr²/2
For 3 semi circle = πr²/2 + πr²/2 + πr²/2 or 3 (πr²/2)
r = 9/2 = 4.5
area of a single semi circle = (3.14 × 4.5²)/2
area of a single semi circle = (3.14 × 20.25 ) /2
area of a single semi circle = 63.585 /2
area of a single semi circle = 31.7925
Area for 3 semi circles = 31.7925 × 3 = 95.3775 ft²
Area of the composite figure = 95.3775 ft² + 81 ft² = 176.3775 ft
Area of the composite figure ≈ 176 ft²
