how would you find the range of this function? g(x)=8-2x-x^2

Question

campbell_st · Answer

well its a parabola thats concave down. 

so I'd start by finding the line of symmetry. 

given a parabola 

$$y = ax^2 + bx + c$$

the line of symmetry is 

$$x = \frac{-b}{2a}$$

so in your question 

$$x = \frac{2}{-2}$$

line of symmetry is x = -1

the maximum value the curve gets to is on the line of symmetry. So substitute x = -1 into the equation 

y = 8 -2(-1) - (-1)^2    so y = 9

the vertex of the parabola is (-1, 9)

the maximum value the curve gets to is y = 9

 so the range is all values of y less than or equal to 9

softballgirl372015 · Answer

omg thank you sooo much!!!!