A bicycle’s wheel has a radius of 32.5 cm. What distance will the bicycle travel if the wheel turns 100,000 times?
2 answers:
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Given the vertex, (2, -4) as the minimum point, and that it is an upward-facing parabola that passes point (1, -2):
We could substitute these values into the vertex form of the quadratic function,
f(x) = a(x - h)^2 + k
where:
(h,k) is the vertex
The axis of symmetry is the vertical line x = 2
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we’ve established these definitions, we can substitute the given values into the vertex form:
f(x) = a(x - 2)^2 - 4
In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:
f(x) = a(x - 2)^2 - 4
-2 = a(1 - 2)^2 - 4
-2 = a(-1)^2 - 4
-2 = a - 4
Add 4 to both sides to solve for “a”
-2 + 4 = a - 4 + 4
2 = a
Now that we have the value of a = 2, we can establish our quadratic function in vertex form:
f(x) = 2(x - 2)^2 - 4
I’m also including a screenshot of the graph of the function we came up with.
Please mark my answers as the Brainliest if you find my explanations helpful :)
We could substitute these values into the vertex form of the quadratic function,
f(x) = a(x - h)^2 + k
where:
(h,k) is the vertex
The axis of symmetry is the vertical line x = 2
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we’ve established these definitions, we can substitute the given values into the vertex form:
f(x) = a(x - 2)^2 - 4
In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:
f(x) = a(x - 2)^2 - 4
-2 = a(1 - 2)^2 - 4
-2 = a(-1)^2 - 4
-2 = a - 4
Add 4 to both sides to solve for “a”
-2 + 4 = a - 4 + 4
2 = a
Now that we have the value of a = 2, we can establish our quadratic function in vertex form:
f(x) = 2(x - 2)^2 - 4
I’m also including a screenshot of the graph of the function we came up with.
Please mark my answers as the Brainliest if you find my explanations helpful :)
<span>This pattern consists of three-fourths of a circle of radius 14 feet and one-fourth of a circle of radius 7 feet. What area of grass can Dan Perkins goat eat?</span>
We know that the formula for the area of the pitch circle are:
where alpha is the pinch of circle, r is radius, and pi is mathematics constant approximately equal 3,14
We know that the formula for the area of the pitch circle are: