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3 years ago

What does the blank equal??

Mathematics

2 answers:

kolbaska11 [484]3 years ago

5 0

Answer:

To a power, elevated to something

Lynna [10]3 years ago

4 0

To power or elevated something

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HELP PLEASE!!!!!!!!!!!

emmainna [20.7K]

Answer:

Part 1) $y=-x^{2}$ ---> Translated up by 1 units

Part 2) $y=x^{2}+1$ ---> Reflected across the x-axis

Part 3) $y=-(x+1)^{2}-1$ ---> Translated left by 1 unit

Part 4) $y=-(x-1)^{2}-1$ ----> Translated right by 1 unit

Part 5) $y=-x^{2}-1$ ----> Reflected across the y-axis

Part 6) $y=-x^{2}-2$ ----> Translated down by 1 unit

Step-by-step explanation:

we know that

The parent function is

$y=-x^{2}-1$ ----> this is a vertical parabola open downward with vertex at (0,-1)

<em>Calculate each case</em>

Part 1) Translated up by 1 unit

The rule of the translation is

(x,y) -----> (x,y+1)

(0,-1) ----> (0,-1+1)

(0,1) ----> (0,0) ----> the new vertex

The new function is equal to

$y=-x^{2}$

Part 2) Reflected across the x-axis

The rule of the reflection is

(x,y) -----> (x,-y)

(0,-1) ----> (0,1) ----> the new vertex

The new function is equal to

$y=x^{2}+1$

Part 3) Translated left by 1 unit

The rule of the translation is

(x,y) -----> (x-1,y)

(0,-1) ----> (0-1,-1)

(0,1) ----> (-1,-1) ----> the new vertex

The new function is equal to

$y=-(x+1)^{2}-1$

Part 4) Translated right by 1 unit

The rule of the translation is

(x,y) -----> (x+1,y)

(0,-1) ----> (0+1,-1)

(0,1) ----> (1,-1) ----> the new vertex

The new function is equal to

$y=-(x-1)^{2}-1$

Part 5) Reflected across the y-axis

The rule of the reflection is

(x,y) -----> (-x,y)

(0,-1) ----> (0,-1) ----> the new vertex

The new function is equal to

$y=-x^{2}-1$

Part 6) Translated down by 1 unit

The rule of the translation is

(x,y) -----> (x,y-1)

(0,-1) ----> (0,-1-1)

(0,1) ----> (0,-2) ----> the new vertex

The new function is equal to

$y=-x^{2}-2$

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