Question

Help on an essay question.
Part 1: Solve each of the quadratic equations below. Show your work.

x2 − 16 = 0 and x2 = −2x + 24

Part 2: Describe what the solution(s) represent to the graph of each.

Part 3: How are the graphs alike? How are they different?

Answer 1

I already solved the first equation I just can't solve the second one.

Answer 2

Well for the second equation make it equal 0 and make sure your a is positive.
\[x^{2} = −2x + 24\]
Subtract
\[x^{2}\]
On both sides.
\[0 = -x^{2}-2x+24\]
Multiply both sides by -1

\[0=x^{2}+2x-24\]
Now can you solve it?

Answer 3

\[\frac{ -b \pm \sqrt{b^{2}-4ac}}{ 2a }\]

Answer 4

Still can't solve it? I feel so stupid. I got as far as you got with the multiplying it by -1 but can't go any further?

Answer 5

Well your
a=1
b=2
c=-24

Answer 6

But what do I do with that?

Answer 7

\[\frac{ -2 \pm \sqrt{2^{2}-4(1)(-24)} }{ 2(1) }\]
\[\frac{ 2 \pm \sqrt{4-(-96)} }{ 2 }\]
\[\frac{ 2 \pm \sqrt{100} }{ }\]
\[\frac{ 2 \pm 10 }{ 2 }\]

Answer 8

So
\[\frac{ 2+10 }{ 2 }=6\]
\[\frac{ 2-10 }{ 2 }=-4\]
So x = 6, and x = -4

Answer 9

Make sense?

Answer 10

No. sorry. I am only in the ninth grade doing algebra.

Answer 11

You're supposed to take Algebra I in 9th grade.

Answer 12

So for the equation you have
\[x^{2}+2x-24=0\]
So this is what it would look like if I wrote the parent function.
\[ax^{2}+bx+c=0\]
To solve the quadratic equation you use this, the quadratic formula.
\[x=\frac{ -b \pm \sqrt{b^{2}-4ac}}{ 2a }\]
So for our equation
\[x^{2}+2x-24=0\]
a=1
b=2
c=-24
So when we plug it in to the quadratic formula (as I showed you above it shows you what x equals.

Answer 13

Making a little more sense to you?

Answer 14

I think so.

Answer 15

So x = 1?

Answer 16

No I solved it for you x=6 and x=-4

Answer 17

Well I have to go to a class now. So if you need more help ask jim_thompson5910

Answer 18

But a is a negative 1

Answer 19

a can't be negative. As I have said above.
Well for the second equation make it equal 0 and make sure your a is positive.
x^2=−2x+24

Subtract x^2 on both sides.

0=−x2−2x+24

Multiply both sides by -1

0=x^2+2x−24
Now put the 0 on the other end.

x^2+2x−24=0
Now your a is positive and your b is now positive and your c is negative.

Answer 20

I got it now thank you