Question

Can someone please help me with these two quadratic equations? I kind of understand how to do it but I can't seem to get the right answers.
1. Solve 2x^2 - 8x = -7

2. If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = -16t2 + 64t + 4.

Answer 1

2x^2 - 8x = -7
put into standard form by add + 7 to both sides.
you will get
2 x^2 -8 x + 7=0

now use the quadratic formula.
see http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/using-the-quadratic-formula

Answer 2

I know the formula. I always have trouble plugging the numbers into the formula.

Answer 3

for the problem 2 x^2 -8 x + 7=0

what is a, b and c ?

Answer 4

A=2 B=-8 and C=7 is that correct?

Answer 5

so far, so good

now write down the quadratic formula with the letters
then underneath it, write it again, but replace the letters with numbers
don't do any arithmetic. just write it down.

Answer 6

\[\frac{ -b+-\sqrt{b^2-4AC} }{ 2a }\]

Answer 7

looks good. now replace the letters with the numbers
A=2 B=-8 and C=7

Answer 8

\[\frac{ -8+-\sqrt{-8^2-4(2)(7)} }{ 2(2) }\]

Answer 9

to do this part correctly, we have to be careful of the minus signs

the formula wants -b
b= -8
put b in parens, like this: (-8)
now use that to replace b in the formula

-b becomes -(-8)

notice that is not what you have.
-(-8) is the same as +8 or just 8

Answer 10

also, inside the square root, write b^2 as (-8)^2 (which means -8 *-8)

Answer 11

Is this correct?

\[\frac{ -(-8)+-\sqrt{-8^2-4(2)(7)} }{ 2(2) }\]

Answer 12

almost, inside the square root, write it (-8)^2

Answer 13

Is that right now lol?
\[\frac{ -(-8)+-\sqrt{(-8)^2-4(2)(7)} }{ 2(2) }\]

Answer 14

perfect.

now let's concentrate on the stuff inside the square root
can you simplify the (-8)^2 - 4(2)(7) ?

Answer 15

I'll be right back.. please don't leave, it'll only take me 20 minutes

Answer 16

message me when you get back

Answer 17

okay I am back, thank you for waiting.
I simplified whats inside the square root and got \[2\sqrt{2}\]
Is that correct?

Answer 18

yes. almost done

simplify the -(-8) out front to + 8
you now have
\[ \frac{8 ± 2 \sqrt{2}}{2\cdot 2} \]

Answer 19

yes, btw in the equation editor if you click on the top row, it brings up a list of operators, one of which is ±

but to continue. you can divide top and bottom by 2
to get one form of the answer

Answer 20

can you show me how the equation should look when you divide the top and bottom.
I don't think i did it right. I got \[\frac{ 1 }{ 4 }(4+\sqrt{2}\]

Answer 21

my answer options are
A. \[-2\pm \sqrt{2} \]
b. \[-2\pm2\sqrt{2}\]
c. \[\frac{ 2\pm \sqrt{2} }{ 2 }\]
d.\[2\pm \frac{ \sqrt{2} }{ 2 }\]

Answer 22

remember when adding or subtracting fractions you need a common denominator?

for example
\[ \frac{3}{4} - \frac{1}{4} = \frac{3 -1}{4} \]
notice we can "go backward" and write
\[ \frac{3 -1}{4}=\frac{3}{4} - \frac{1}{4} \]

use that same idea with
\[ \frac{8 ± 2 \sqrt{2}}{2\cdot 2} = \frac{8}{2\cdot 2}± \frac{2\sqrt{2}}{2\cdot 2}\]

Answer 23

now you have two separate divide problems
8/4
and the other term

Answer 24

I got \[\frac{ 8 }{ 2*2 }=2 & \frac{ 2\sqrt{2} }{ 2*2 }=\frac{ \sqrt{2} }{ 2 }\]

Answer 25

\[\frac{ 8 }{ 2*2 }=2 \]

Answer 26

looks correct.

Answer 27

and
\[\frac{ 2\sqrt{2} }{ 2*2 }=\frac{ \sqrt{2} }{ 2 }\]

Answer 28

so the answer would be \[2\pm \frac{ \sqrt{2} }{ 2 }\]
and be D.

Answer 29

yes

Answer 30

Also, even though I HATE not doing my own work can you pretty please just give me the answer to -->
If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = -16t2 + 64t + 4
a. \[2\pm \frac{ \sqrt{17} }{ 2 }\]
b.\[\frac{ 2\pm \sqrt{17} }{ 2 }\]
c. \[2\pm4\sqrt{17}\]
d.\[\frac{ 16\pm \sqrt{17} }{ 2 }\]

Answer 31

h = -16t^2 + 64t + 4

the height h = 0 when on the ground
so you must solve
-16t^2 + 64t + 4 =0

the first thing you can do is divide both sides (all terms by 4) to simplify it
-4 t^2 + 16 t + 1 = 0

now use the quadratic formula.

Answer 32

actually that is all I need. Word problems aren't my strong. But after you got it looking right and all the help you already gave me its no problem.
THANK YOU! You have no idea how much you helped.