Algebra 2 Question?

First, let's change the second function to a quadratic equation:

f(x) = 2(x-3)^2-9

f(x) = 2(x^2 - 6x + 9) - 9 [squared the x-3]

f(x) = 2x^2 - 12x + 18 - 9 [multiplied what's in parentheses by 2]

f(x) = 2x^2 - 12x + 9 [18-9 is 9]

So, the place or places where these two functions intersect is going to be the places where they are equal to one another. So let's set them equal to one another.

-2x + 3 = 2x^2 - 12x + 9

Now, we'd like to get everything on one side of the equation, leaving a zero on the other side.

3 = 2x^2 - 10x + 9 [moved the -2x]

0 = 2x^2 - 10x + 6 [moved the 3]

And, switch it around so it looks like a normal quadratic equation.

2x^2 - 10x + 6 = 0

We've got two choices here - we can try to factor it, or we can use the quadratic formula. Factoring ends up not working evenly, so let's plug it into the formula:

-b +/- sqrt( b^2 - 4ac )

------------------------------

2a

-10 +/- sqrt(100 - 4*2*6)

---------------------------------

4

The plus or minus means there are two answers:

( 10 + sqrt(52) ) / 4 = 4.302776

and

( 10 - sqrt(52) ) / 4 = 0.697224

Those will be the x coordinates of your answer (in other words, they are the x's for which both functions will give the same answer). That same answer that the two functions give will be the y coordinates of your answer. You can get the y coordinates by plugging the x coordinates into either function. The first function is much easier, so let's use that:

-2( 4.302776 ) + 3 = -5.605551

and

-2( 0.697224 ) + 3 = 1.605551

So the two possible answers are:

( 4.302776, -5.605551 )

and

( 0.697224, 1.605551 )

Of these, only one of them is in the IVth quadrant - that's the quadrant with a positive x but negative y. The first one is your answer:

( 4.302776, -5.605551 )

Since the answer wants you to round to 1000ths, you get:

( 4.303, -5.606 )

Use the quadratic formula to find the x-value, and then plug that in to either equation for the y-value.

Setting the two equations equal to each other yields

-2x+3 = 2(x-3)^2 - 9

-2x+3 = 2x^2 - 12x + 9

2x^2 - 10x - 12 = 0

You should be able to take it from there.

I am in Algerbra 1 and I know how to solve that question. f(x) is y. They are right you need to use a TI-83 (That's what I have!) Also, combine like terms! (if u can...)

Therefor:

y=-2x+3 and

y=2(x-3)^2-9

use a ti 83 or better calculater and just plot them onto a graph

lmao im in algebra 2 also but idk what the answer is =O