State the vertex of the graph:
y=2x-6x+9
...the 2x is squared.
y = 2x^2 -6x + 9
The vertex is where the function is a minimum. That would be where dy/dx = 4x -6 = 0
x= 3/2
If you are not familiar with calculus, then rewrite the expression
y = 2 (x^2 -3x + (3/2)^2) +9 -(3/2)^2
= 2(x - 3/2)^2 + constant
That has a minimum when x -3/2 = 0
multiply 2 by 2
To find the vertex, we need to find the x-coordinate and y-coordinate of the vertex.
For the given equation, y = 2x^2 - 6x + 9, we can determine the x-coordinate of the vertex by using the formula x = -b/2a, where a is the coefficient of x^2, and b is the coefficient of x.
In this case, a = 2 and b = -6. Plugging these values into the formula, we get x = -(-6)/2(2) = 6/4 = 3/2.
So, the x-coordinate of the vertex is 3/2.
To find the y-coordinate of the vertex, we substitute the x-coordinate back into the equation:
y = 2(3/2)^2 - 6(3/2) + 9
y = 2(9/4) - 18/2 + 9
y = 18/4 - 36/4 + 9
y = -9/4
Therefore, the vertex of the graph is (3/2, -9/4).