Transformations...quad equations (domain and range)...Ten points for first right answer?

Question

OK, I have to describe the transformation

f(x)=-(x-4)^2-3

MY ANSWER
1. Shift 4 units to the rt. on the hor. axis
2. Reflection through the x axis
3. vertical shift down 3 units

AM I RIGHT?

Now, Write the equation for the parabola that is

1. Shifted twenty units left
2. Vertically stretched by a factor of 6
3. Shift up 4 units

IS IT f(x)=6(x+20)+4

AM I RIGHT?

PART DUE!

What are the domain and range of the following quad. equations.

1. f(x)=-(x+7)^2+5

Is it

D=(-infinity, +infinity)...R=[5, +infinity)

IS THIS RIGHT?

and
g(x)=5x^2+25-4
5x^2+21

Well, I'm not sure how to approach this...I know completing the square is necessary but how do I do this one?

THANKS!

Oh thanks Puzzling...I really didn't take into account the - sign and I better tell my teacher about the 25X...THANKS!

Answer 1

PROBLEMS 1 and 2:

You are correct on the first two assuming you meant to have include the square --> 6(x + 20)² + 4

PROBLEM 3:

For the third one, I think I see a negative sign. Shouldn't that mean that the range is:
R = (-infinity, 5]

PROBLEM 4:

Are you sure it isn't the following?
g(x) = 5x² + 25x - 4

Start by pulling out the 5 so you just have x²:

g(x) = 5(x² + 5x) - 4

Now you want to complete the square for x² + 5x. You do this by taking the coefficient on the x term (5), halving it (2.5) and squaring it (6.25). Now add and subtract this inside the parentheses:

g(x) = 5(x² + 5x + 6.25 - 6.25) - 4

Get the -6.25 outside the parentheses by multiplying by 5:

g(x) = 5(x² + 5x + 6.25) - 31.25 - 4

Simplify the terms at the end:
g(x) = 5(x² + 5x + 6.25) - 35.25

And write the parentheses as a perfect square:
g(x) = 5(x + 2.5)² - 35.25

There's the function in vertex form.

Answer 2

Your first answer is correct, well done.
Your second answer is missing a squared sign but correct other than that. Well done.
Part 3.
Your domain is correct however your range is wrong. There is a minus sign in front of the brackets so the Range is (-∞,5]
Part 4. What exactly were you meant to do with this question? Factorise it?
Did you mean? g(x) = 5x² + 25x - 4
As it there is nothing to do with 5x²+21.
g(x) = 5x² + 25x - 4
g(x) = 5(x²+5x) - 4
g(x) = 5(x + 5/2)² - 25/4 - 4
g(x) = 5(x + 5/2)² - 41/4
g(x) = 5[ (x + 5/2)² - 41/20 ]
g(x) = 5[ (x + 5/2 - √[41/20]) (x + 5/2 + √[41/20])

Answer 3

Dont remember much.. Learned this last year, but im pretty sure that it right way 2 go!