PLS HELP BEST ANSWER GETS SHOUTOUT AND BRAINLIEST

Write the algebraic expression that matches each graph:

1. upside down graph: y = - ⎜x +1⎟ + 1

2. regular graph: y =  ⎜x -2⎟ -2

Step-by-step explanation:

This is an absolute value function  f(x) = |x| with some transformations

1) facing down graph means that f(x) is flipped around x-axis so a must be negative

y = -a ⎜x - h⎟ + k

h is the number of units for  f(x) = |x| translated horizontally

h is positive if translation is to the right, h is negative if  translation is to the left

k is the number of units for   f(x) = |x| translated vertically

if translation is up k is positive; if a translation is down k is negative

function i s flipped over x-axis moved 1 unit to the left and 1 unit up

y = - ⎜x +1⎟ + 1

2) similar for this graph

function is 2 units to the right and 2 units down

y =  ⎜x -2⎟ -2

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15