Look at picture
write the equation in vertex form and standard form.

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 2, 2), thus

y = a(x + 2)² + 2

To find a substitute the point on the graph (0, 0) into the equation

0 = a(0 + 2)² + 2

0 = 4a + 2 ( subtract 2 from both sides )

- 2 = 4a ( divide both sides by 4 )

- = a

y = - (x + 2)² + 2 ← in vertex form

Expanding and simplifying gives

y = - (x² + 4x + 4) + 2

  = - x² - 2x - 2 + 2

  = - x² - 2x ← in standard form

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

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y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: