Answer:
(4,1)
Step-by-step explanation:
The vertex of the quadratic can be found using -b/2a. The vertex is the point (-b/2a, f(-b/2a)).
To find the x coordinate of the quadratic, define its a,b, and c. The quadratic has a = 2, b=-16, and c=31. Then -b/2a is -(-16)/2(2) = 16/4 = 4.
To find the y-coordinate, input the x=4 and solve for y.
The vertex is (4,1).
Answer:
The length of the shortest side of the triangle is 10 units.
Step-by-step explanation:
Let <em>a</em> be the shortest side of the isosceles triangle and <em>b</em> be the two congruent sides.
The congruent sides <em>b</em> are each one unit longer than the shortest side. Hence:
The perimeter of the isosceles triangle is given by:
This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be <em>s</em>. Hence:
The perimeter of the square is:
Since the two perimeters are equivalent:
Substitute for <em>b: </em>
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Solve for <em>a</em>. Distribute:
Simplify:
Hence:
The length of the shortest side of the triangle is 10 units.
