The correct question is
<span>
Penelope determined the solutions of the quadratic function by completing the square.f(x) = 4x² + 8x + 1
–1 = 4x² + 8x
–1 = 4(x² + 2x)
–1 + 1 = 4(x² + 2x + 1)
0 = 4(x + 2)²
0 = (x + 2)²
0 = x + 2
–2 = x
What error did Penelope make in her work?
we have that
</span>f(x) = 4x² + 8x + 1
to find the solutions of the quadratic function
let
f(x)=0
4x² + 8x + 1=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(4x² + 8x)=-1
Factor the
leading coefficient
4*(x² + 2x)=-1
Complete the square Remember to balance the equation
by adding the same constants to each side.
4*(x² + 2x+1)=-1+4 --------> ( added 4 to both sides)
Rewrite as perfect squares
4*(x+1)²=3
(x+1)²=3/4--------> (+/-)[x+1]=√3/2
(+)[x+1]=√3/2---> x1=(√3/2)-1----> x1=(√3-2)/2
(-)[x+1]=√3/2----> x2=(-2-√3)/2
therefore
the answer is
<span>
Penelope should have added 4 to both sides instead of adding 1.</span>
Answer:
1.) four and six hundredths
4+.06
2) 5.2 5+.2
3. six and eighty nine hundredths
<h3>Answer: Choice D</h3>
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Explanation:
The long way to do this is to multiply all the fractions out by hand, or use a calculator to make shorter work of this.
The shortest way is to simply count how many negative signs each expression has.
The rule is: if there are an even number of negative signs, then the product will be positive. Otherwise, the product is negative.
For choice A, we have 3 negative signs. The result (whatever number it is) is negative. Choice B is a similar story. Choice C is also negative because we have 1 negative sign. Choices A through C have an odd number of negative signs.
Only choice D has an even number of negative signs. The two negatives multiply to cancel to a positive. The negative is like undoing the positive. So two negatives just undo each other. This is why the multiplied version of choice D will be some positive number.
Or you can think of it as opposites. If you are looking up (positive direction) and say "do the opposite" then you must look down (negative direction). Then if you say "do the opposite", then you must look back up in the positive direction.
