Question

@butterflydreamer can you help me?

Answer 1

okey dokey.
So firstly, we are given the equation in "Standard form" ( y = ax^2 + bx + c ).
\[y = ax^2 + bx + c\]
\[y = -x^2 + 12x - 4 \]
Identify the values of "a" , "b" and "c"

Answer 2

A: -x^2
B: 12x
C: -4

Answer 3

you're close :)
But "a" is just the number in front of "x^2"
SO a = -1

and "b" is just the number in front of "x"
So b = 12

Makes sense? :)

Answer 4

It's starting to.
But, I do understand why "a" is -1 and why "b" is 12.(:

Answer 5

Don't we use the equation:
t= -b/(2a)?

Answer 6

great!
Alrighties soo nooww, we want to find the 'vertex'.
To find the x-coordinate, we use this formula:
\[x = \frac{ -b }{ 2a }\]
So since we know a = -1 and b = 12, plug these values into the formula above.

Answer 7

x = -12/2*-1

Answer 8

correct. Now can you simplify it? :)
\[x = \frac{ -12 }{ 2(-1) } = \frac{ -12 }{ -2 } = ?\]

Answer 9

-6?(:

Answer 10

Remember, the negative signs will cancel out :)

Answer 11

6

Answer 12

yess!
So, we know the x-coordinate of the vertex = 6
Now to find the y-coordinate of the vertex, sub x = 6 into the equation
"y = -x^2 + 12x - 4"

\[y = - (6^2) + 12(6) - 4\]
Now, plug the values into your calculator to find y

Answer 13

32?

Answer 14

yyupp! ^_^
So now we have know the vertex is at (6, 32)

Okay so now we want to write the equation in "vertex form"
\[y = a(x - h)^2 + k\]
Where the vertex has coordinates:
\[(h, k)\]

*note: we already found all the values of a, h and k so just plug it into the equation*

So what would the equation be in vertex form?

Answer 15

y=-1(6-32)^2+32?
I got the -1 from when we first started.

Answer 16

you're close : )yes a = -1
vertex is (h , k ) where we found the vertex was ( 6 , 32) right?
So what is "h" and what is "k"?

Answer 17

h:6
k:32

Answer 18

OH, I didn't notice that "x" that is where I made the mistake

Answer 19

yes! :)
Now we ONLY sub in the values of a, h and k into y = a ( x - h )^2 + k
a = -1, h = 6 , k = 32

therefore the equation would be?

Answer 20

Y=-1(x-6)^2+32

Answer 21

correeecctt :D!
Also, \[y = -1 (x -6 )^2 + 32\] can also be written as:
\[y = -(x-6)^2 + 32\]

Answer 22

Can you help me with one more question, please?(:

Answer 23

suree

Answer 24

We're given the equation:
\[y = x^2 + 2x - 8 \]
To find the "zeroes", we let y = 0. Therefore:
\[x^2 + 2x - 8 = 0\]
Now, we want to factor the equation into the form ( x ) ( x ) = 0
So what are the factors of 8?

Answer 25

4 and 2?

Answer 26

yes :)
but we know that 4 and 2 when MULTIPLIED must give you -8 and when added together, must give you a positive 2.
so would the 4 or the 2 be negative?

Answer 27

-4 because it is the larger number and when multiplied, it is -8.

Answer 28

hmm but does -4 + 2 = 2 ?

Answer 29

No, it equals -2

Answer 30

exactly!
So -4 and 2 would not work :)

Try 4 and -2.
4 * -2 = -8 right?
does 4 + (-2) = 4 - 2 = 2 ?

Answer 31

Yes.

Answer 32

okay so that means, we will be using 4 and -2.
So when we factorise
\[x^2 + 2x - 8 = 0\]

we get:
\[(x−2)(x+4)=0\]


Now from here, this means that we will have two values of x.
(x - 2) = 0
Therefore x -2 = 0
x = ?

or

(x + 4 ) = 0
therefore x + 4 = 0
x = ?

Answer 33

I'm confused.

Answer 34

about which part?

Answer 35

About what I am solving for.

Answer 36

you are solving for the zeroes of the function.
This means when y = 0 , what are the value(s) of x.
SO since we had the equation: \[y = x^2 + 2x - 8\]
We plug in y = 0 and we get
\[x^2 + 2x - 8 = 0\]
From here, we want to find the values of x.
Therefore, we used factoristion and ended up with:
\[(x - 2 ) ( x + 4 ) = 0\]

From here, to find the values of x , we know that EITHER (x - 2) = 0 or (x + 4) = 0
E.g.
If x - 2 = 0
Add 2 to both sides
x = 2 right?
So if we subbed it back into the equation we would get ( 2 - 2) ( 2 + 4) = 0 which is correct right?

If x + 4 = 0
what would x = ?

Answer 37

So, x would equal 8 because you're adding 4 to both sides?

Answer 38

x = 2 is ONE value of x.

To find the 2nd value of x.
We ONLY focus on x + 4 = 0 (don't use x = 2)
Subtract 4 from both sides and x = ?

Answer 39

-4?

Answer 40

yes :)
Here's a drawing to help show you the working out