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

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.

Sure! Let's go through each question and find the answers step by step:

1. To determine whether the graph of y = x – 3x^2 + 5 has a maximum or minimum, we need to look at the coefficient of the x^2 term, which is -3.

If the coefficient is positive (greater than 0), the graph opens downwards and has a maximum point.
If the coefficient is negative (less than 0), the graph opens upwards and has a minimum point.

In this case, since the coefficient -3 is negative, the graph opens upwards, indicating that it has a minimum point.

2. The given equation is y = -2(x - 3)^2 + 4. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Comparing the given equation with the vertex form, we can identify that the vertex is located at the point (3, 4). Therefore, the vertex of the graph is (3, 4).

3. Similar to question 1, the graph of y = -2(x - 3)^2 + 4 will open upwards or downwards depending on the coefficient of the x^2 term.

Since the coefficient -2 is negative, the graph opens upwards. Thus, the graph opens up.

To summarize:
1. The graph of y = x – 3x^2 + 5 has a minimum.
2. The vertex of the graph of y = -2(x - 3)^2 + 4 is (3, 4).
3. The graph of y = -2(x - 3)^2 + 4 opens upward.

I hope this explanation helps! Let me know if you have any further questions.