Algebra, 90 points! factor 4x²+20x factor x²+9x+8 solve 4r² -16=84 find the solution to the following equation by transferring it into a perfect square trinomial x²-6x=27 use the quadratic formula to solve 3y²-9y-30=0 where is the vertex of the parabola y=x^2+6x+7 in which direction does the parabola open? y=3x²+5x+10

#1:  4x(x+5)
#2:  (x+8)(x+1)
#3:  r=5
#4:  x=9
#5:  y=-2 or y=5
#6:  (-3, -2)
#7:  It opens upward.

To factor #1, pull out what each has in common; both are divisible by 4 and both have an x, so pull 4x out:
4x(x+5)

To factor #2, find factors of c (8) that sum to b (9).  The only factors of 8 that will sum to 9 are 8 and 1:
(x+8)(x+1)

To complete the square on #3, we divide b by 2 and square it:  (-6/2)² = (-3)² = 9.  Add this to both sides:
x²-6x+9=27+9
(x-3)²=36

Take the square root of both sides, and we have
x-3=6
x = 9

Using the quadratic on #4,


To find the vertex on #5, use x=-b/2a:
x = -6/2(1) = -6/2 = -3

Now substitute this back into the equation to solve for y:
y=(-3)²+6(-3)+7=9-18+7=-2

This makes the vertex (-3, -2)

For #6, it opens upward since the coefficient of a is positive.