Question

Identify the vertex for the graph of y = −3x2 + 6x − 4.

Answer 1

magic formula for vertex is \(-\frac{b}{2a}\) for the first coordinate
second coordinate is what you get when you repalace \(x\) by \(-\frac{b}{2a}\)

Answer 2

To find the x cord of the vertex use \[ -\frac{b}{2a} \]
Just plugin your b value and a value
\[ -\frac{6}{2(-3)} = 1\]
\[ x = 1\]
Now put the value of x, which is 1 in to the x variable of the equation for find y
\[ y = −3x^2 + 6x − 4 \]
\[ y = −3(1)^2 + 6(1) − 4 \]
[ y = -1 \]

So our vertex is at (1,-1)

Also the parabola will open down since a(-3) is a negative and we will have a maximum.