f(x) + n - shift a graph of f n units up
f(x) - n - shift a graph of f n units down
f(x + n) - shift a graph of f n units left
f(x - n) - shift a graph of f n units right.
f(x) = x³, g(x) = (x - 2)³ - 3 = f(x - 2) - 3
2 units right and 3 units down.
What is the value for this?
2 answers:
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( + 4)(
- 4)
To solve this question you must FOIL (First, Outside, Inside, Last) like so
First:
(x^2 + 4)(x^2 - 4)
x^2 * x^2
x^4
Outside:
(x^2 + 4)(x^2 - 4)
x^2 * -4
-4x^2
Inside:
(x^2 + 4)(x^2 - 4)
4 * x^2
4x^2
Last:
(x^2 + 4)(x^2 - 4)
4 * -4
-16
Now combine all the products of the FOIL together like so...
x^4 - 4x^2 +4x^2 - 16
Combine like terms:
x^4 - 4x^2 +4x^2 - 16
- 4x^2 +4x^2 = 0
x^4 - 16 <<<This is your answer
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
3.58
Step-by-step explanation:
Given :
y = 2x + 4 -------- eq1
y = 2x - 4 -------- eq2
sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.
Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2
This gives us y = 2(-2) + 4 = 0
Hence we get a point (x,y) = (-2,0)
Step 2: express equation 2 in general form (i.e Ax + By + C = 0)
y = 2x-4 -------rearrange---> 2x - y -4 = 0
Comparing with the general form, we get A = 2, B = -1, C = -4
Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).
substituting the values for A, B, C and (x, y) from the previous step:
d = | (2)(-2) + (-1)(0) + (-4) | / √(2² + (-1)²)
d = | -4 + 0 - 4 | / √(4 + 1)
d = | -8 | / √5
d = 8 / √5
d = 3.5777
d = 3.58 (rounded 2 dec. pl)
