Question

Identify the vertex for the graph of y = −3x2 + 6x − 2.

(1, 1)

(−1, 1)

(1, −5)

(−1, −5)

Answer 1

\[f(x)= −3x^2 + 6x − 2\]
Find the derivative of f(x) and set it to zero. Solve for x then.

Answer 2

Afterwards if you want your y you simply plug the x you found to the original function f(x)

Answer 3

Do you understand what you need to do?

Answer 4

uhm a little..

Answer 5

Well to give you a little more insight of this we want to find the vertex. That's when the line changes from negative to positive or vice versa.

Answer 6

oh alright thank you

Answer 7

That arrow points to the vertex. We can graph it and estimate where the vertex is but the best way to do this is by finding the derivative of the function....why does this work? Well the thing is that when you take the derivative we know that whatever value for x that makes the function zero will tell us where the curve changes.

After we find the x all we can do is plug in the x we found to the original function

Answer 8

So all we are doing is finding the center of the curve.

Answer 9

so what is the center of the curve?

Answer 10

I don't know....I didn't solve it....I told you how to do it. Find the derivative ...set it to zero and solve for x

Answer 11

-6x + 6 = 0
x = 1

y = -3 x 1 + 6 x( 1) -2 = 1

Answer 12

thank you everyone for the help

Answer 13

To find the vertex use the formula below to find the x vertex point of y = −3x^2 + 6x − 2
\[x = \frac{-b}{2a} \]
Plug our points in the the formula
\[x = \frac{-(+6}{2(-3)} \]
\[x = \frac{-6}{-6} \]
x = 1 //This is our x vertex
Now we have the x coord (1, ?) we need to find the y coord
To find the y coord just plug our x coord, which is -1 into the equation
\[y = -3x^2 + 6x - 2\]
\[y = -3(1)^2 + 6(1) - 2\]
\[y = -3 + 6 - 2\]
\[y = 3 - 2\]
y =1 //This is our y vertex point
Now we have x and y so our vertex is at (1, 1)