Identify the range of the equation y = −x2 − 12x + 3.

All real numbers

y ≤ 39

y ≥ −6

y ≤ −105

Question

Identify the range of the equation y = −x2 − 12x + 3. 

 All real numbers 

 y ≤ 39 

 y ≥ −6 

 y ≤ −105

campbell_st · Answer

the parabola is concave down 

find the vertex 

the y value in the vertex will be the maximum value in the range. 

there are 2 ways... the easiest is to find the line of symmetry and then substitute that value into the equation to find the maximum value... 

line or symmetry

$$x = \frac{-b}{2a} $$

in your question b = -12 and a = -1 

so x = -6

substitute it to find the max value and the range will be all values of y less than or equal to that value