Write the formula for absolute value function if its graph has the vertex at point (−2,5) and passes through the point (3,−10).

Question

Please tell me what the formula is if it starts with y= 

Answer 1

The parent function of an absolute value function is y = |x| which has it's vertex at the origin (0,0).  Moving the vertex to (-2, 5) means you moved it 2 to the left and 5 up.  So the equation adjusts to y = |x + 2| + 5.  Now, this function won't go through (3, -10) since it opens up and would need to open down and be stretched.  So we need to put a multiplier in front to fix it: y = a|x + 2| + 5

 

By plugging in (3, -10) for x and y, we can solve for a:

 

-10 = a|3+2| +5

-10 = a|5| + 5

-10 = 5a + 5

-15 = 5a

-3 = a

 

Therefore the equation is: y = -3|x + 2| + 5

Answer 2

The formula (function) is

y=-3|x+2|+5