Math help!!!!!!!!!!?

Question

1. Write the equation y= -(x+7)(x+3) in:
A)vertex form
B)factored Form

Answer 1

A) by vertex form I'm assuming that's y = a(x-h)^2 + k

y = -(x^2 + 10x + 21)
y = -(x^2 + 10x +___) - 21 moving the 21 out of the ( ) with - in front

completing the square, (1/2)(10)^2 = 25 so add this into the () and subtract back out at end

y = -(x^2 + 10x + 25) -21 -(-25) (neg 25 because of the - on ()

y = -(x + 5)^2 + 4

B) the original problem is in factored form.

The only thing different that might be done is that the vertex form your text has is the y = -x^2 - 10x - 21 that you would just get by FOIL-ing the problem. Then the factored form is what I put in in part A.

The text I use for teaching and have always seen these called were standard form and general form. Thus I apologize if my forms are different

Answer 2

PART A:

Expand the equation using FOIL:
y = -(x² + 3x + 7x + 21)

Group all the x² and x terms together and simplify:
y = -(x² + 10x) - 21

Complete the square by taking the x-coefficient (10), halving it (5) and squaring it (25). Add this and subtract it inside the parentheses:

y = -(x² + 10x + 25 - 25) - 21

Take the -25 out side the parentheses and simplify:
y = -(x² + 10x + 25) + 25 - 21
y = -(x² + 10x + 25) + 4

Finally write the expression in the parentheses as a perfect square:

y = -(x + 5)² + 4

Done! This is in vertex form of:
y = a(x - h)² + k

a = -1, h = -5, k = 4

PART B:

It already *is* in factored form. And you have expanded form above, if that was what they were asking.