You can put this solution on YOUR website! The y intercept is easy just let x=0
=0^2-6x0+4
=4
Y intercept is 4.
For the vertex you use a method called "completing the square"
First step is to take out the coefficient of x^2 which is 0 in this case. so we can skip this step.
Next take the coefficient of x and divide it by 2. Then 'inject' that into the x^2.
So instead of (x)^2 it's (x-6/2)^2 which is (x-3)^2 simplified.
Now add the y intercept so it's y=(x-3)^2 + 4.
If you expand (x-3)^2 it's x^2-6x+9 and that 9 was never there in the beginning equation so to rebalance the equation you need to remove 9 so,
y=(x-3)^2 + 4 - 9. Which becomes y=(x-3)^2 -5.
Now let (x-3)^2 = 0
so solving for x x=3
Now solcing for y, y = -5
so the vertex = (3,-5)
Now let y = 0 to find x intercept
so 0=(x-3)^2 -5
so 5=(x-3)^2
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