Answer:
Step-by-step explanation:
Step 1: Define
Difference Quotient: 
f(x) = -x² - 3x + 1
f(x + h) means that x = (x + h)
f(x) is just the normal function
Step 2: Find difference quotient
- <u>Substitute:</u>
![\frac{[-(x+h)^2-3(x+h)+1]-(-x^2-3x+1)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B-%28x%2Bh%29%5E2-3%28x%2Bh%29%2B1%5D-%28-x%5E2-3x%2B1%29%7D%7Bh%7D)
- <u>Expand and Distribute:</u>
![\frac{[-(x^2+2hx+h^2)-3x-3h+1]+x^2+3x-1}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B-%28x%5E2%2B2hx%2Bh%5E2%29-3x-3h%2B1%5D%2Bx%5E2%2B3x-1%7D%7Bh%7D)
- <u>Distribute:</u>
- <u>Combine like terms:</u>
- <u>Factor out </u><em><u>h</u></em><u>:</u>
- <u>Simplify:</u>
Answer:
"Starting today, I need to forget what's gone. Appreciate what still remains and look forward to what's coming next."
"Pain makes you stronger, fear makes you braver, heartbreak makes you wiser."
"I will not allow myself to not feel chosen every single day. And I’ll wait till whenever that is." — Hannah Brown
"Sometimes good things fall apart so better things can come together."
"Live for what today has to offer, not for what yesterday has taken away."
"Accept what is, let go of what was, and have faith in what will be."
"Don't be afraid to start over. It’s a brand new opportunity to rebuild what you truly want."
"Inhale the future, exhale the past."
"Don’t cry because it’s over, smile because it happened."
Answer:
y = 4x + -9
Step-by-step explanation:
The y intercept which is -9, is the point in which the graph crosses the x-axis
In order to find the slope we need to identify two clear points on the graph.
- (0, -9)
- ( 1, -5)
Now that we have our two points we need to find the distance between them.
As you can see on the attachment the distance between the two points is 4 units up and 1 unit to the right, therefore the slope is 4/1 = 4.
Final Answer: y = 4x + -9
Answer:
y = 1/4 x - 2
Step-by-step explanation:
To write the equation of a line, find from the line the slope and y-intercept. The y-intercept is where the line crosses the y-axis which here is at point (0,-2).
The slope of the line is found by writing a ratio between the vertical distance and the horizontal distance between points.
Slope is 1/4.
Substitute m = 1/4 and b = -2 into the slope intercept form y = mx + b.
y = 1/4 x - 2
Answer:
8
Step-by-step explanation:
we know that
The rate of change of a linear equation is a constant that is the same that the slope
step 1
we have
The equation of the graph (function 1) is equal to
y=4
Is a horizontal line
The slope is equal to zero
so
The rate of change of function 1 is zero
step 2
The equation of the function 2 is
This is a linear equation in slope intercept form
where
the slope is equal to m=8
so
The rate of change of function 2 is 8
therefore
The rate of change of function 2 is 8 more than the rate of change of function 1
