Question

Can someone walk me through the steps of this quadratic formula?

-x^2-3+5=0

Thank you!

Answer 1

yes, i assume you have the formula with you...
could you find the values of a,b,c in it ?

Answer 2

and i also assume its \(-x^2-3x+5=0\)

Answer 3

If it is like the first formula, I would start with
-x^2+3-5=0 I think

Answer 4

\(\large x= \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Answer 5

I am unfamiliar with using variables with this formula.

Answer 6

compare your equation with \(ax^2+bx+c=0\)
what you get as values of a,b,c ?

Answer 7

Standard form of a parabola \[ax ^{2}+bx+c\]

Answer 8

BTW so you mean -x^2-3x+5 instead of -x^2-3+5?

Answer 9

Do** not so

Answer 10

-x^2-3+5=0 is the formula is that what you meant?

Answer 11

okay well that simplifies to -x^2+2 and to find what a b and c are we are going to compare -x^2+2 to \[ax ^{2}+bx+c\]

Answer 12

Ok, I am writing the steps so that I can complete the other problems on my own.

Answer 13

I'm going to start over and write in steps for you!

Answer 14

That would be great!

Answer 15

Step 1: write quadratic equation! \[\frac{-b \pm \sqrt{b ^{2}-4(a)(c)}}{ 2a }\]

Answer 16

Step two: compare your function \[-x ^{2}+2\] in this case with \[a x^{2}+bx+c\]

Answer 17

Step 3: find a,b, and c
\[-x ^{2}+2\] has an "a" of -1, a "b" of 0, and a "c" of 2
Tell me if you understand where I got that from.

Answer 18

You are following the formula that you wrote first ax^2+bx+c

Answer 19

Right! Okay let's move on

Answer 20

Step 4: plug your values of a, b, and c into the quadratic equation.
a=-1 b=0 c=2, and plug them into the quadratic equation of \[\frac{ -b \pm \sqrt{b ^{2}-4(a)(c)} }{ 2a }\]

then we get \[\frac{ 0\pm \sqrt{0-4(-1)(2)} }{ 2(-1) }\]

Answer 21

Step 5: simplify
\[\frac{ 0\pm \sqrt{0-4(-1)(2)} }{ 2(-1) } = \frac{ 0\pm \sqrt{8} }{ -2 }\]

Answer 22

Step 6: evaluate \[0+ -\frac{ \sqrt{8} }{ 2 } = -\frac{ \sqrt{8} }{ 2 } and 0 - -\frac{ \sqrt{8} }{ 2 } = \frac{ \sqrt{8} }{ 2 }\]

Answer 23

Or you could use decimals sqrt(8)= 2.83
(2.83)/-2= -1.42 then we would have
\[0+(-1.42)= -1.42 \] and \[0-(-1.42)= 1.42\]

Answer 24

Step 7: understand what we just found!

We found the points where this parabola crosses the x-axis, also known as the x-intercepts!

Answer 25

I will use step 6 because I understood every step that you wrote. Thank you for Step 7 because I could never make this connection before now. I will work these problems in the math lab now. Thank you and here is your medal!

Answer 26

Thanks man good job. If you wanna see what we just did go to https://www.desmos.com/calculator and type in -x^2+2, then put your mouse over the points where the graph crosses the x axis!

Answer 27

I will do that, you have just gotten a new fan! Thank you!

Answer 28

Glad to help!

Answer 29

It will take me a lot longer to solve but I now have the complete formula! Thanks again!

Answer 30

:)