Given:
The image of a lens crosses the x-axis at –2 and 3.
The point (–1, 2) is also on the parabola.
To find:
The equation that can be used to model the image of the lens.
Solution:
If the graph of polynomial intersect the x-axis at c, then (x-c) is a factor of the polynomial.
It is given that the image of a lens crosses the x-axis at –2 and 3. It means (x+2) and (x-3) are factors of the function.
So, the equation of the parabola is:
...(i)
Where, k is a constant.
It is given that the point (–1, 2) is also on the parabola. It means the equation of the parabola must be satisfy by the point (-1,2).
Putting
in (i), we get
![2=k(-1+2)(-1-3)](https://tex.z-dn.net/?f=2%3Dk%28-1%2B2%29%28-1-3%29)
![2=k(1)(-4)](https://tex.z-dn.net/?f=2%3Dk%281%29%28-4%29)
![2=-4k](https://tex.z-dn.net/?f=2%3D-4k)
Divide both sides by -4.
![\dfrac{2}{-4}=k](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B-4%7D%3Dk)
![-\dfrac{1}{2}=k](https://tex.z-dn.net/?f=-%5Cdfrac%7B1%7D%7B2%7D%3Dk)
Putting
in (i), we get
![y=-\dfrac{1}{2}(x+2)(x-3)](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B1%7D%7B2%7D%28x%2B2%29%28x-3%29)
Therefore, the required equation of the parabola is
.
Note: All options are incorrect.
Answer: Collins has 1/2 of an apple left.
Step-by-step explanation:
Collins shared 4/8 of an apple with two siblings, and these pieces add up to 1/2, so 1 - 1/2 = 1/2 apples.
340 = 100%
34 = 10% (Divide 100% digit by 10 to get 10%)
102 = 30% (Multiply 10% by 3)
340 + 102 = 442 ( To get 130%, which is 100% with the 30% increase)
442 = 130%
Hope this helped!
The volume of a triangular prism is the area of the base multiplied by the height.
<u>Let's first identify our values:</u>
20 cm = height of prism
12 cm = base of triangle
10 cm = height of triangle
First, we need to calculate the area of the triangle. To calculate the area of the triangle, we multiply the base of the triangle by the height of the triangle. In this case, the base is 7 and the height is 5 so 7 × 5 = 35 and then we divide 35 by 2 and we will get a quotient of 17.5.
Finally, we will multiply the area of the triangle which is 17.5 by 12.
17.5 × 12 = 210
.
Therefore, the area of the triangular prism is 210
.
(2,-7) is the point after the translation is made to find the original point just do the opposite of the equation so for x it would be
2-4=-2
Y would be
-7+3=-4
So the answer is (-2,-4)