Question

Please help, algebra, 90 points!

Answer 1

#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,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\y=\frac{--9\pm \sqrt{(-9)^2-4(3)(-30)}}{2(3)} \\ \\=\frac{9\pm \sqrt{81--360}}{6}=\frac{9\pm \sqrt{441}}{6} \\ \\=\frac{9+21}{6}\text{ or }\frac{9-21}{6}=\frac{30}{6}\text{ or }\frac{-12}{6} \\ \\=5\text{ or }-2$

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.

Answer 2

You have a lot of questions here, I will help with the first three:

Factor:

4x^2 + 20x     Factor out a 4x
4x(x + 5)

x^2 + 9x + 8   You have to work backwards with FOIL here
(x + 1)(x + 8)


Solve:

4r^2 - 16 = 84
4r^2 = 100
r^2 = 25

r = 5 or r = -5