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Answer:
y = (x + 9)² + 9
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a parabola in standard form : ax² + bx + c : a ≠ 0
the the x-coordinate of the vertex is
= -
y = x² + 18x + 90 is in standard form
with a = 1, b= 18 and c = 90
= -
= - 9
to find the corresponding y-coordinate substitute x = - 9 into the equation
y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9
⇒ y = (x + 9)² + 9 ← in vertex form
Considering the figures, the area that will be painted is of 38.9 square feet.
<h3>What is the area of a rectangle?</h3>
The area of a rectangle of length l and width w is given by:
The area of a triangle of base b and height h is given by:
The area of a semi-circle of radius r is given by:
In this problem:
- The rectangle with l = 6 ft and w = 8 ft will be painted, along with the triangle of dimensions b = 8 ft and h = 4 ft.
- The semi-circle with r = 4 ft will not be painted.
Hence, the area that will be painted, in square feet, is given by:
More can be learned about the area of a figure at brainly.com/question/10489198