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!
The first answer is correct
C(2, -2) D(-1, -2)
because the line from point a to point b is 3 units long and 3 x 4 = 12 (area) (and 12/3=4) so, the points that are exactly 4 units down from point a and point b would be the correct answer - (2, -2) and (-1, -2)
Answer:
The bottom two are your answers.
Step-by-step explanation:
What you do is use the slope formula which is y_2-y_1/x_2-x_1.
So for PQ it will be 12(which is y_2)-6(which is y_1)/4(which is x_2)-5(which is x_1) which equals -6.
12-6/4-5=-6.
The answer is A because when the two lines are on the outside of a term like that it means that what ever is inside is the opposite of the original number
For ex. | 4 | < 4
The 1st number will be a negative so it makes the statement true
