# Thread: Algebra 2 (Help me for the love of God!)

1. I need some help on about five questions... The first two I need to find a quadratic equation that has the give roots:
The first question: 3/4, 9/2
The second question: -0.25, 0.25

Then next three I need to write each equation in the form f(x) = a(x-h)^2+k (unless it's not already in that form). I need to name the vertex, axis of symmetry, and direction of opening for the graph of eahc quadratic function. Then I need to graph it.
The third question is: f(x)=a(x-5)^2-7
The fourth question is: f(x)= -9^2+54x-8
The fifth (and final) question is: f(x)=0.25x^2-6x-16  2.

3. Originally Posted by EAfreak
I need some help on about five questions... The first two I need to find a quadratic equation that has the give roots:
The first question: 3/4, 9/2
The second question: -0.25, 0.25
Simplicity itself: let me give you an example 4, -1.45
I simply write (x-4)(x-(-1.45)) = 0
now if x is 4 or -1.45 I get 0
I can multiply this out using (a+b)(c+d)= ac+ad+bc+bd
x^2 - 2.55 x - 5.8 = 0 Originally Posted by EAfreak
Then next three I need to write each equation in the form f(x) = a(x-h)^2+k (unless it's not already in that form). I need to name the vertex, axis of symmetry, and direction of opening for the graph of eahc quadratic function. Then I need to graph it.
The third question is: f(x)=a(x-5)^2-7
The fourth question is: f(x)= -9^2+54x-8
The fifth (and final) question is: f(x)=0.25x^2-6x-16

Again an example: f(x)=x^2 - 2.55 x - 5.8
The process is known as completing the square
and it uses (a-b)^2 = a^2 -2ab + b^2
where in our f(x), a^2 = x^2 and 2ab = 2.55 x
This means that a=x and b = 2.55/2 = 1.275
so (x-1.275)^2 = x^2 -2.55 x + 1.625625
So we take or f(x) and add (x-1.275)^2 and subtract x^2 -2.55 x + 1.625625 to get (x-1.275)^2 -5.8 -1.625625
Since what we added and subtracted are equal it is still f(x)
So f(x) = (x-1.275)^2 - 7.425625

SO the vertex of the parabola is at (1.275, -7.425625)
The axis of symmetry is x = 1.275
and the parabola opens upward because comparing
f(x) = (x-1.275)^2 - 7.425625 to f(x) = a(x-h)^2+k
we see that a = +1 which is positive  4. For a quadratic equation of the form x^2 + bx + c = 0
The sum of its two roots is -b
The product of its two roots is c.

the first equation is:
x^2 -(3/4 + 9/2) + (3/4)*(9/2) = 0
x^2 - (21/4)x + 27/8 = 0
8x^2 - 42x + 27 = 0

The second equation is
x^2 +(0.25 - 0.25)x +0.25*(-0.25) = 0
x^2 - 1/16= 0
16x^2 - 1 = 0

************************************************** *
Write equations in the form f(x) = a(x-h)^2+k.

The fourth equation:
-9x^2+54x-8
= -9(x^2 - 6x + 8/9)
= -9[(x^2 - 6x + 9) - 9 + 8/9]
= -9[(x - 3)^2 - 9 + 8/9]
= -9(x - 3)^2 + 81 - 8
= -9(x - 3)^2 + 73

The fifth equation
0.25x^2-6x-16
= 0.25[x^2 - 24x - 64]
= 0.25[(x^2 - 24x + 144) - 144 -64]
= 0.25)[(x -12)^2 - 208]
= 0.25(x - 12)^2 - 52  5. orca: On this forum, we prefer not to answer homework questions, but rather we attempt to help people by providing examples (as mitchellmckain did) or by asking leading questions. Of course, we're excited to have you on the math forum--just keep this in mind for the future!  6. I need Algebra/ Algebra 2 Help?

imagery numbers

i(2+i)

(-3+7i)(1-2i)

(3-2i)²

completing the square

(7x+2)²=110

graph the equation

y=-x²-4x-1

y > 2x²+4x-1

I have tried to do the problems up above but I always keep getting the wrong answer when I check in the back of the book. Please help me understand what I am doing wrong.

Thank you  Bookmarks
 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement