This Question is in multiple sections.

f(x)= -2x^2+2x+10 is the problem
1)What is the x coordinate of vertex in simplified fraction?
2)What is the y coordinate of vertex in simplified fraction?
3)What is the line of symmetry?
4)What is the maximum/minumum of f(x)?
5)The value of f(1/2)=21/2 is minimum or maximum?

Can you please explain these steps to me in detail so that I get it. I'm preparing for a final in a couple days and have a couple last minute questions about certain problems on my algebra before I do my final. Thank You!!!

1). Put the equation in the form of

y= a(x-h)^2+k

Then the vertex will be at h,k

y=-2(x^2-x-5)=-2(x^2-x+1/4)+10+1/2
y=-2(x-1/2)^2+ 10.5
so h=1/2, k= 10.5
line of symettry is as x=h
max.min is at x=h, so max is 10.5

Thank you!!!! Now, can you please tell me how to choose the correct graphing without actually seeing everything right in front of you?

Sure! I'd be happy to explain each step in detail. Let's go through each question one by one:

1) To find the x-coordinate of the vertex, we first need to identify the correct formula to use. In this case, the formula for the x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).

Comparing it with our equation f(x) = -2x^2 + 2x + 10, we can see that a = -2 and b = 2. Plugging these values into the formula, we get x = -2 / (2 * -2) = -1/2. So, the x-coordinate of the vertex is -1/2.

2) To find the y-coordinate of the vertex, we substitute the x-coordinate (-1/2) into the equation f(x) = -2x^2 + 2x + 10. So, f(-1/2) = -2 * (-1/2)^2 + 2 * (-1/2) + 10 = -2(1/4) - 1 + 10 = -1/2 - 1 + 10 = 9/2. Therefore, the y-coordinate of the vertex is 9/2.

3) The line of symmetry is a vertical line that passes through the vertex of the parabola. In our case, since the x-coordinate of the vertex is -1/2, the line of symmetry is x = -1/2.

4) If the coefficient of x^2 (the 'a' value) is positive, the parabola opens downwards, so the vertex represents the maximum point. Conversely, if the coefficient of x^2 is negative, the parabola opens upwards, and the vertex represents the minimum point. In our equation, since the coefficient of x^2 is -2 (negative), the parabola opens upwards, and the vertex represents the minimum point.

5) We can evaluate f(1/2) to determine whether it represents the minimum or maximum. Substituting x = 1/2 into the equation f(x) = -2x^2 + 2x + 10, we get f(1/2) = -2(1/2)^2 + 2(1/2) + 10 = -2(1/4) + 1 + 10 = -1/2 + 1 + 10 = 21/2.

Since the parabola opens upwards, the vertex represents the minimum point, and f(1/2) = 21/2 is the minimum value of the function.

I hope this explanation helps you understand the steps! Good luck with your final exam! If you have any more questions, feel free to ask.