Question

You must show your work on each of the following questions.

1. Rewrite y = x^2 + 14x + 29 in general form.
2. Rewrite y = 3x^2 - 24x + 10 in general form.
3. Solve for x: (x - 9)^2 = 1
4. Solve for x: x^2 + 24x + 90 = 0
5. Solve for x: 2x^2 - 4x - 14 = 0
6. Create your own quadratic equation and demonstrate how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.

Answer 1

1....already in general form.

2. ...already in general form

Answer 2

3)\[(x-9)^2=1\]
\[(\sqrt{(x-9)^2}=\sqrt{1}\]
x-9=1
x=1+9,x=10

Answer 3

4)
the general solution using the quadratic equation is:
\[x=\frac{ -24\pm \sqrt{(2-24)^2-(4*1*90)} }{ 2*1 }=\frac{ -24\pm \sqrt{216} }{ 2 }\]
\[x=\frac{ -24\pm6\sqrt{6} }{ 2 }\]
\[x=-12\pm3\sqrt{6}\]

Answer 4

5)
the general solution using the quadratic equation is:
\[x=\frac{ 4\pm \sqrt{(-4)^2-(4*2(-14))} }{2*2 }=\frac{ 4\pm \sqrt{128} }{ 4}\]
\[x=1\pm2\sqrt{2}\]

Answer 5

6)
x^2 - 6x = 0
by graphing:

Answer 6

x=6,x=0

Answer 7

by factoring:
x(x-6)=0
x=0 or x-6=0
x=6

Answer 8

by the quadratic formula:
\[x=\frac{ 6\pm \sqrt{(-6)^2-(4*1*0)} }{2*1}=\frac{ 6\pm6 }{ 2 }\]
x=0,x=6

Answer 9

by completing the square:
x^2 - 6x +(-6/2)^2= (-6/2)^2
x^2-6x+(-6/2)^2=9
(x+(-6/2))^2=9
(x-3)^2=9
x-3=3,x=6
or
x-3=-3,x=0

Answer 10

@touseii45 get it.

Answer 11

I get the most of it (: thank you so very much! @ASAAD123

Answer 12

welcome ^-^.