Answer:
The scale factor is 4
Step-by-step explanation:
Divide one of the sides on the larger shape with the corresponding side on the smaller shape. So if you choose the top one you would to 40/10 which is 4.
Answer:
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
General Formulas and Concepts:
<u>Algebra I</u>
Equality Properties
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
- a = vertical shrink/stretch
- b = horizontal shrink/stretch
- c = horizontal movement left/right
- d = vertical movement up/down
Step-by-step explanation:
<u>Step 1: Define</u>
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
<u>Step 2: Write Vertex Form</u>
- Define: f(x) = a(bx - c)² + d
- Substitute: f(x) = -1/3(x + 12)² + 9
<u>Step 3: Write Standard Form</u>
- Define: f(x) = -1/3(x + 12)² + 9
- Expand: f(x) = -1/3(x² + 24x + 144) + 9
- Distribute -1/3: f(x) = -1/3x² - 8x - 48 + 9
- Combine like terms: f(x) = -1/3x² - 8x - 39
And we have our final answers!
Answer:
Step-by-step explanation:
See the figure below.
This is how you graph directly from the equation in the slope-intercept form (y = mx + b) without having to create a table of x and y values.
The equation is
y = -2/3 x + 1
Compare it with
y = mx + b
b = 1
The y-intercept is 1, so mark 1 on the y-axis. (You already did.)
I placed a black dot there.
The slope is m.
m = -2/3
slope = m = rise/run
A slope of -2/3 can be though of as -2 rise and 3 run. That means start from the y-intercept, and go -2 in y (a rise of 2 down) and 3 in x (a run 3 right). Point graphed in red.
Mathematically, -2/3 is the same as 2/(-3), so starting again from the y-intercept, this slope can also be though of as rise of 2 in y (a rise of 2 up) and a run of -3 in x (a run of 3 left). Point graphed in green.
The line is graphed in blue.
It’s equals x=1 hope that helps
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