SOLUTION: What is the range of y = -x^2 - 2x + 3 A. x ≤ 4 B. x ≤ -4 C. y ≤ 4 D. y ≥ -4

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: What is the range of y = -x^2 - 2x + 3 A. x ≤ 4 B. x ≤ -4 C. y ≤ 4 D. y ≥ -4      Log On


   

Question 1206757: What is the range of y = -x^2 - 2x + 3
A. x ≤ 4
B. x ≤ -4
C. y ≤ 4
D. y ≥ -4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+-x%5E2+-+2x+%2B+3
you have an upside down parabola which have a max at vertex, so the range will be all y less and equal to the y coordinate of the vertex
find vertex
y+=+-%28x%5E2+%2B2x%2Bb%5E2%29-%28-b%5E2%29+%2B+3....b=1

y+=+-%28x%5E2+%2B2x%2B1%5E2%29%2B1%5E2+%2B+3
y+=+-%28x%2B1%29%5E2%2B4

vertex is at (-1,4)
so, the range is
{ y element R : y%3C=4 }

+graph%28+600%2C+600%2C+-10%2C+5%2C+-10%2C+10%2C+-x%5E2+-+2x+%2B+3%29+

answer: C. y%3C=4