Answer:
B
Step-by-step explanation:
-4/2 = -2
-2 + 5 = 3
Answer:
the inverse for each relation:
1. {(1,-2), (2, 3),(3, -3),(4, 2)} is
<u>{</u><u>(</u><u>-</u><u>2</u><u>,</u><u>1</u><u>)</u><u>,</u><u>(</u><u>3</u><u>,</u><u>2</u><u>)</u><u>,</u><u>(</u><u>-</u><u>3</u><u>,</u><u>3</u><u>)</u><u>,</u><u>(</u><u>2</u><u>,</u><u>4</u><u>)</u><u>}</u><u>.</u>
There are 12 outcomes. The coin can land on either heads or tails, and then you can extract any number from 1 to 6 from the box. So, the outcomes are
- Heads, 1
- Heads, 2
- Heads, 3
- Heads, 4
- Heads, 5
- Heads, 6
- Tails, 1
- Tails, 2
- Tails, 3
- Tails, 4
- Tails, 5
- Tails, 6
Given:
A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8).
To find:
The corresponding quadratic expression.
Solution:
If graph of a function intersect the x-axis at c, then (x-c) is a factor of the function.
A quadratic function has x-intercepts 2 and 6. It means (x-2) and (x-6) are two factors of the required quadratic function.
The function is defined as:
...(i)
Where, a is a constant.
The vertex of the quadratic function is (4,8). It means the point (4,8) will satisfy the function.
Substituting x=4 and P(x)=8 in (i).
![8=a(4-2)(4-6)](https://tex.z-dn.net/?f=8%3Da%284-2%29%284-6%29)
![8=a(2)(-2)](https://tex.z-dn.net/?f=8%3Da%282%29%28-2%29)
![8=-4a](https://tex.z-dn.net/?f=8%3D-4a)
Divide both sides by -4.
![\dfrac{8}{-4}=a](https://tex.z-dn.net/?f=%5Cdfrac%7B8%7D%7B-4%7D%3Da)
![-2=a](https://tex.z-dn.net/?f=-2%3Da)
Putting
in (i), we get
![P(x)=-2(x-2)(x-6)](https://tex.z-dn.net/?f=P%28x%29%3D-2%28x-2%29%28x-6%29)
![P(x)=-2(x^2-6x-2x+12)](https://tex.z-dn.net/?f=P%28x%29%3D-2%28x%5E2-6x-2x%2B12%29)
![P(x)=-2(x^2-8x+12)](https://tex.z-dn.net/?f=P%28x%29%3D-2%28x%5E2-8x%2B12%29)
![P(x)=-2x^2+16x-24](https://tex.z-dn.net/?f=P%28x%29%3D-2x%5E2%2B16x-24)
Therefore, the correct option is B.