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!
(24-2)180=3960 the answer is 3960
Answer:
57-48
Step-by-step explanation:
9
Answer:
<h2><u>Supplementary</u></h2><h2><u>x = 34</u></h2>
Explanation:
- Supplementary angles: Angles that measure up to 180°
- Write an equation to find x
4x + 10 + x = 180
4x + x + 10 = 180
5x + 10 = 180
- Subtract 10 from both sides
5x + 10 - 10 = 180 - 10
5x = 170
5x / 5 = 170 / 5
x = 34
3/24 would be down to 1/8 so 3/24 is smaller
