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a_sh-v [17]
3 years ago
6

What is the equation of a parabola in vertex form for a line that passed through (5,-4) and has vertex (-2,5)

Mathematics
1 answer:
Ahat [919]3 years ago
5 0

\text{The vertex form of a parabola}\\\\y=a(x-h)^2+k\\\\\text{We have the vertex}\ (-2,\ 5)\to h=-2,\ k=5.\\\\\text{Substitute}\\\\y=a(x-(-2))^2+5=a(x+2)^2+5\\\\\text{We have the point}\ (5,\ -4).\\\text{Substitute the coordinates of the point to the equation:}\\\\-4=a(5+2)^2+5\\\\-4=a(7)^2+5\\\\-4=49a+5\qquad|-5\\\\-9=49a\qquad|:49\\\\a=-\dfrac{9}{49}\\\\Answer:\ \boxed{y=-\dfrac{9}{49}(x+2)^2+5}

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Answer: 225 square feet

Step-by-step explanation:

We find the area of the 4 triangle and the area of the rectangle and thereafter we add everything together.

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Area of triangle 2 = area of triangle 1= 48( because the opposite triangle are congruent so they have equal base and height)

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Area of triangle 4=Area of triangle 3 = 57 (the opposite triangle are congruent and so they have the same base and height hence the same area)

Area of the rectangle = length×breadth

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Total surface area = addition of all the areas of the triangles and the rectangle

Total surface area= 48+48+57+57+72 = 225

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