Answer:
33
Step-by-step explanation:
33 appears most.
Answer:
C:-4x+2
Step-by-step Explanation:
![x + 4 - 5x - 2 \\ = x - 5x + 4 - 2 \\ = - 4x + 2 \\](https://tex.z-dn.net/?f=x%20%2B%204%20-%205x%20-%202%20%5C%5C%20%20%3D%20x%20-%205x%20%2B%204%20-%202%20%5C%5C%20%3D%20%20%20-%204x%20%2B%202%20%5C%5C%20)
Answer:
![D = 0](https://tex.z-dn.net/?f=D%20%3D%200)
The graph has 1 x-intercept
Step-by-step explanation:
Given
![f(x) = -4x^2 + 12x - 9](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-4x%5E2%20%2B%2012x%20-%209)
Required
- Discriminant of f
- Number of x intercepts
Let D represent the discriminant;
D is calculated as thus
![D = b^2 - 4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E2%20-%204ac)
Where a, b and c are derived from the following general format;
![f(x) = ax^2 + bx +c](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2Bc)
By comparing
with ![f(x) = -4x^2 + 12x - 9](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-4x%5E2%20%2B%2012x%20-%209)
We have
![f(x) = f(x)\\ax^2 = -4x^2\\bx = 12x\\c = -9](https://tex.z-dn.net/?f=f%28x%29%20%3D%20f%28x%29%5C%5Cax%5E2%20%3D%20-4x%5E2%5C%5Cbx%20%3D%2012x%5C%5Cc%20%3D%20-9)
Solving further;
![a = -4\\b=12\\c=-9](https://tex.z-dn.net/?f=a%20%3D%20-4%5C%5Cb%3D12%5C%5Cc%3D-9)
So, D can now be calculated;
becomes
![D = 12^2 - 4 * -4 * -9](https://tex.z-dn.net/?f=D%20%3D%2012%5E2%20-%204%20%2A%20-4%20%2A%20-9)
![D = 144 - 144](https://tex.z-dn.net/?f=D%20%3D%20144%20-%20144)
![D = 0](https://tex.z-dn.net/?f=D%20%3D%200)
Hence, the discriminant of f is 0
From the value of the discriminant, we can determine the number of x intercepts of the graph;
When D = 0, then; there exists only one x-intercept and it as calculated as thus
![x = \frac{-b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%7D%7B2a%7D)
Recall that
![a = -4\\b=12\\c=-9](https://tex.z-dn.net/?f=a%20%3D%20-4%5C%5Cb%3D12%5C%5Cc%3D-9)
So,
becomes
![x = \frac{-12}{2 * -4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-12%7D%7B2%20%2A%20-4%7D)
![x = \frac{-12}{-8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-12%7D%7B-8%7D)
![x = \frac{12}{8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B12%7D%7B8%7D)
![x =1.5](https://tex.z-dn.net/?f=x%20%3D1.5)
It is none of them
9x³ - 4x³ = 5x³
3x² - -2x² = 3x²+2x² = 5x²
-3 - 16 = 13
So :
5x³ + 5x² +13