Question

What is the equation of the following graph?

Answer 1

Hang on, I need to attach a file first.

Answer 2

The possible answers are:

A: f(x) = x^2 + 10x -24
B: f(x) = -x^2 +10x -24
C: f(x) = x^2 -10x +24
D f(x) = -x^2 +10x +24

Answer 3

HI!!

Answer 4

Hello. Welcome, I was just asking around for help on this particular problem.

Answer 5

it is a parabola that opens down, so the leading coefficient is negative
skip C

Answer 6

next lets find the vertex

Answer 7

So I should skip C and A given those are both positive?

Answer 8

which you see by your eyeballs is \((5,1)\)

Answer 9

Yes, I see that.

Answer 10

that means it looks like
\[(x-5)^2+1\]

Answer 11

multiply out, see which one you get

Answer 12

I would get x^2 +25 +1. Which would be x^2+26.

Answer 13

\[(x-5)(x-5)+1\\
x^2-20x+25+1\\
etc\]

Answer 14

x^2 - 20x +26?

Answer 15

which is none of your answers, so i would say there is a mistake in the question

Answer 16

Yes, I believe so. So out of the answers that are possible, we've ruled out C, right?

Answer 17

ooh doe i made a mistake!!

Answer 18

\[-(x-5)^2+1\] there

Answer 19

Okay, I guess we could start again then.

Answer 20

\[-(x-5)(x-5)+1\\
-x^2+10x-25+1\\
-x^2-10x-24\]

Answer 21

That would be -x^2 -25 +1, which would be -x^2 -24?

Answer 22

don't forget the \(+10x\)

Answer 23

\[-x^2+10x-24\] if you do the algebra

Answer 24

-x^2 +10x - 24 is my answer? So that would mean B, then.

Answer 25

i forgot the minus sign in front of the whole thing

Answer 26

yeah, B

Answer 27

Oh, very well. Thank you for helping me work through this process.

Answer 28

http://www.wolframalpha.com/input/?i=-x%5E2%2B10x-24

Answer 29

\[\color\magenta\heartsuit\]

Answer 30

Thank you for helping me.

Answer 31

Now, there is something we have to begin to analyze here.
A parabola is always formed by a quadratic formula, and it opens upwards or downwards depending on the sign of the coeficent that the x squared have.
if it's positive, it opens upwards and when it's negative, it opens downwards.

A quadratic formula, in a factorized form, looks like:
\[f(x)=(x \pm P) ( x \pm Q)\]
Where "P" and "Q" are the x-intercepts, pretty much the "roots" of the equation.
Wich makes it zero.

Now, another important thing, the form I gave you, is a form that represents a parabola with the vertex that belongs in the y-axis.
So, in order to pivot it on the x-axis, we will take the f(x+c) and it0ll move on the sides.
Like this:
\[f(x+c)=((x \pm c) \pm P)((x \pm c ) \pm Q)\]
That would be the form of a function that has been moved in the x-axis.