Which of the following values has 4 significant figures?
1 answer:
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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 :)
ANSWER
EXPLANATION
We want to factor
out of
The first term is already having a factor of
The constant term which is the second term is not having a factor of
so we need to use a trick of multiplying and dividing by the same factor to obtain,
We can now factor
out of the right hand side to obtain,
Let us rewrite the right most fraction using the normal division symbol.
We simplify to obtain,
This further gives us,
EXPLANATION
We want to factor
out of
The first term is already having a factor of
The constant term which is the second term is not having a factor of
so we need to use a trick of multiplying and dividing by the same factor to obtain,
We can now factor
out of the right hand side to obtain,
Let us rewrite the right most fraction using the normal division symbol.
We simplify to obtain,
This further gives us,