Find all solutions to 3x^2 + 2x + 1 = 0

Question

anonymous · Answer

Please help.

anonymous · Answer

According to discriminant b^2-4ac. (2)^2 - 4*(3)*1 = -8 < 0 therefore no solutions. See  for yourself on the graph. It never touches 0.

anonymous · Answer

Thank you SO much:) can you help me with some more?

anonymous · Answer

Sure, bring it on

anonymous · Answer

Charlie uses the function f(x) = 2x^2 + 5x + 3 to track the temperature of a substance, where x represents the time. When you evaluate f(5) you find that the temperature of the substance is 78°C. What is the domain of the situation of Charlie's quadratic function?

anonymous · Answer

The function has real values for any x value, so the domain is all real x.

anonymous · Answer

However, you might want to argue that since the time can never be negative, the domain is x ≥ 0

anonymous · Answer

Thank you, I wish I was good in math..Write the quadratic function in vertex form.
f(x) = x^2 - 3x - 10

anonymous · Answer

Hmmm, never come across vertex form. Will look it up

anonymous · Answer

Thank you!

anonymous · Answer

OK.

Put all the numbers (with no x's) on one side with the y

x^2 - 3x = y + 10

Start off by completing the square. (what value of ? will make the LHS a perfect square)

x^2 - 3x + ? = y + 10 + ?

? = (3/2)^2 = 9/4

x^2 - 3x + 9/4 = y + 10 + 9/4
(x - 1.5)^2 = y + 12.25

And I believe this is now in vertex form

anonymous · Answer

Or you could do:
y = (x - 1.5)^2 - 12.25

anonymous · Answer

Thank you!  The parabola with the equation y = x^2 was both horizontally and vertically translated to produce the parabola with the equation y = x^2 – 14x + 39. Which statement is true?
	

A)
	The parabola with the equation y = x^2 was translated 7 units to the left and 10 units down. 	
	

B)
	The parabola with the equation y = x^2 was translated 7 units to the left and 10 units up. 	
	

C)
	The parabola with the equation y = x^2 was translated 7 units to the right and 10 units down. 	
	

D)
	The parabola with the equation y = x^2 was translated 7 units to the right and 10 units up.

anonymous · Answer

ahh. Step 1 FACTORISE

anonymous · Answer

No, actually not yet

anonymous · Answer

so dont factor

anonymous · Answer

I'm thinking...

anonymous · Answer

x^2 – 14x + 39 = (x^2 - 14x + 49) + 39
                        = (x-7)^2 - 10
so then we have y = (x-7)^2 - 10
rearrange:
y + 10 = (x - 7)^2

Now, the negatives of the numbers are the answers:

it moved the graph 10 down the y-axis
and 7 right across the x-axis

If its a quadratic, you want to get it into (x+?)^2 form.