SOLUTION: I need to find out the maximum or minimum of the function f(x)=-2x^2+4x+8. Then, I have to find the domain and range. So far, I have found that the domain equals all real numbers.

Question 531804: I need to find out the maximum or minimum of the function f(x)=-2x^2+4x+8. Then, I have to find the domain and range. So far, I have found that the domain equals all real numbers.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
I need to find out the maximum or minimum of the function f(x)=-2x^2+4x+8. Then, I have to find the domain and range. So far, I have found that the domain equals all real numbers.
**
Standard form of equation for a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. If the lead coefficient<0, parabola opens downward, that is, it has a maximum.
For given equation: f(x)=-2x^2+4x+8, parabola opens downward.
By inspection you can see there are no restrictions, so the domain is all real numbers as you stated. To find the range, we need to find the maximum and you can do this by completing the square.
y=-2x^2+4x+8.
y=-2(x^2-2x+1)+8+2
y=-2(x-1)^2+10
vertex: (1,10)
maximum at 10
ans:
Range: (-∞,10)
Domain(-∞,∞)
RELATED QUESTIONS
For the function f(x)= -3x^2-4x+3, find the minimum or maximum value and where it occurs. (answered by robertb)

Find the maximum or minimum value of the function. f(x)= -x^2/3+2x+6 (it's -x^2 over 3 (answered by stanbon)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by solver91311)

F(x)=2x^2-4x-5 Does this function have a maximum or minimum value What is the... (answered by josgarithmetic)

I NEED MORE SPECIFICS ON HOW TO FIND THE DOMAIN AND RANGE OF THE FOLLOWING FUNCTION:... (answered by stanbon)

Find the minimum or maximum value of the given function. Then state the domain and range (answered by solver91311)

How do I figure this out?!?! "Determine without graphing, whether the quadratic function... (answered by Nate)

I need to find out the domain and range of f(x)=(1/2)log( x -... (answered by tommyt3rd)

Hi there tutors, I have a question that I don't know how to do. This is the equation :... (answered by KMST)