Question

I posted these a little while ago but this time I have answered them.
1. Does the graph of y = x – 3x2 + 5 have a maximum or minimum?

2. What is the vertex of the graph of y = -2(x - 3)2 + 4?

3. Does the graph of y = -2(x - 3)2+ 4 open up or down?
My answers: 1. I cannot answer. This is the one I need help with because I don't know how to tell if it has a maximum or minimum. It wasn't in my notes. 2. 1 3. it opens up.

Could someone check 2. &3 and help me with 1? Thanks

Answer 1

2 and three are wrong. On three, what happens to y as x gets large? On two, the axis of symettry is x=3. What is y when x is three?

1. factor it.
y= -3 (x^2 -1/3 x + ?) + 5+?

now, the question mark is what it takes to make a perfect square, 1/2 of 1/3 squared, or 1/36)
y= -3(x-1/6)^2 + 5 1/36

Now, it opens downward, so it has a maximum.
later on, in calculus, there are other methods to determine max/min.