SOLUTION: Which statement is true about this function f(x)= -4x^2-8x+4 a) the range is less than or equal to 4 b) the range is less than or equal to 8 c) the domain is greater than or equ

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Which statement is true about this function f(x)= -4x^2-8x+4 a) the range is less than or equal to 4 b) the range is less than or equal to 8 c) the domain is greater than or equ      Log On


   



Question 935284: Which statement is true about this function f(x)= -4x^2-8x+4
a) the range is less than or equal to 4
b) the range is less than or equal to 8
c) the domain is greater than or equal to 0
d) the domain is greater than or equal to -1

Found 3 solutions by Rosseta786, MathLover1, MathTherapy:
Answer by Rosseta786(21) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+-4x%5E2-8x%2B4
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-4x%5E2-8x%2B4%29+
domain: R, all real numbers
interval: (-infinity,infinity)
range:
{ f%28x%29 element R : f%28x%29%3C=8 }
(-infinity,8]
so, your answer is: b) the range is less than or equal to 8

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Which statement is true about this function f(x)= -4x^2-8x+4
a) the range is less than or equal to 4
b) the range is less than or equal to 8
c) the domain is greater than or equal to 0
d) the domain is greater than or equal to -1

f%28x%29+=+-+4x%5E2+-+8x+%2B+4
Since a < 0, the parabola y will have a maximum
x-coordinate of vertex: x+=+-+b%2F2a______x+=+-+%28-+8%29%2F2%28-+4%29_____x+=+8%2F%28-+8%29________x+=+-+1
f%28x%29+=+-+4x%5E2+-+8x+%2B+4
With x-coordinate of the vertex of the parabola at: x+=+-+1, its y-coordinate is:
f%28-+1%29+=+-+4%28-+1%29%5E2+-+8%28-+1%29+%2B+4, or f%28-+1%29+=+-+4+%2B+8+%2B+4, or f%28-+1%29+=+8
Thus, the range of the parabola will be: highlight_green%28y+%3C=+8%29