In exact form: 13/36
in decimal form: 0.36111111...
complette the square to get vertex form or y=a(x-h)^2+k
(h,k) is vertex
1. group x terms, so for y=ax^2+bx+c, do y=(ax^2+bx)+c
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2, factor out the leading coefinet (constant in front of the x^2 term), basicallly factor out a
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3. take 1/2 of the linear coefient (number in
front of the x), and square it ,then add negative and positive of it
inside parnthases
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4. complete the squre and expand
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so
y=-1/4x^2+4x-19
group
y=(-1/4x^2+4x)-19
undistribute -1/4
y=-1/4(x^2-16x)-19
take 1/2 of -16 and squer it to get 64 then add neg and pos inside
y=-1/4(x^2-16x+64-64)-19
factorperfect square
y=-1/4((x-8)^2-64)-19
expand
y=-1/4(x-8)^2+16-19
y=-1/4(x-8)^2-3
vertex is (8,-3)
Moved 5 units right.......................
Answer:
the distance between the points is about 9.2 units
Step-by-step explanation:
It is well you should not understand it. <em>No question is asked</em>.
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The answer choices suggest you are to find the distance between the two points. There is only one choice in a reasonable range: 9.2 units.
Each point is more than 2 units from any axis, so 2 units is clearly not the answer. The size of the graph is much less than 81 units, so clearly that is not the answer.
The difference of coordinates in the x-direction is 6; in the y-direction the difference is 7 units. The distance between the points will be more than the longest of these (7) and less than about 1.5 times that (10.5). Only one choice is in this range: 9.2 units.
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The Pythagorean theorem is used to calculate the distance between points. The distance is considered to be the hypotenuse of a right triangle with legs of lengths equal to the differences of coordinates. Here, that means the distance (d) is ...
d² = 6² + 7² = 36 +49 = 85
d = √85 ≈ 9.2 . . . . grid squares, or "units"
