Answer:
ƒ(x) = (x - 2)^2 + 1
Step-by-step explanation:
To make f(x) be a translation of the graph of g(x) by (h, k), write it as ...
f(x) = g(x -h) +k
You want to translate g(x) = x^2 by (2, 1), 2 units right and 1 unit up, so the function f(x) is ...
f(x) = g(x -2) +1
f(x) = (x -2)^2 +1
it would be 1/3 because there independent variables
<span>sqrt(3x+7)=x-1 </span>One solution was found : <span> x = 6
</span>Radical Equation entered :
<span> √3x+7 = x-1
</span>
Step by step solution :<span>Step 1 :</span>Isolate the square root on the left hand side :
Radical already isolated
<span> √3x+7 = x-1
</span>
<span>Step 2 :</span>Eliminate the radical on the left hand side :
Raise both sides to the second power
<span> (√3x+7)2 = (x-1)2
</span> After squaring
<span> 3x+7 = x2-2x+1
</span>
<span>Step 3 :</span>Solve the quadratic equation :
Rearranged equation
<span> x2 - 5x -6 = 0
</span>
This equation has two rational roots:
<span> {x1, x2}={6, -1}
</span>
<span>Step 4 :</span>Check that the first solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in 6 for x
<span> √3•(6)+7 = (6)-1
</span> Simplify
<span> √25 = 5
</span> Solution checks !!
Solution is:
<span> x = 6
</span>
<span>Step 5 :</span>Check that the second solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in -1 for x
<span> √3•(-1)+7 = (-1)-1
</span> Simplify
<span> √4 = -2
</span> Solution does not check
2 ≠ -2
One solution was found : <span> x = 6</span>
There must be two binomial factors. Thus, we eliminate Answer A, which contains only one such factor.
(x-3)(x+3) has the form (a-b)(a+b), which equals a^2 - 3^2. This is a special product. Eliminate Answer B, because a^2 - 3^2 does not equal x^2 - 6x + 9.
The middle term of x^2 - 6x + 9 is negative. This quadratic has the form x^2 - y^2, which is special product and whose factors are (x-y) and (x-y).
Thus, x^2-6x+9 = (x-3)(x-3) (Answer C)
