Millimeter centimeter meter kilometer
C by AA- bc 180 degrees in a triangle
Answer:
![y=-6x+2](https://tex.z-dn.net/?f=y%3D-6x%2B2)
Step-by-step explanation:
Hi there!
Slope-intercept form:
where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when x=0)
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
where two points that fall on the line are
and ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
Given the graph, we determine which points we could use. For example, we could use the two points
and
:
![m=\displaystyle \frac{-4-2}{1-0}\\\\m=\displaystyle \frac{-6}{1}\\\\m=-6](https://tex.z-dn.net/?f=m%3D%5Cdisplaystyle%20%5Cfrac%7B-4-2%7D%7B1-0%7D%5C%5C%5C%5Cm%3D%5Cdisplaystyle%20%5Cfrac%7B-6%7D%7B1%7D%5C%5C%5C%5Cm%3D-6)
Therefore, the slope of the line is -6. Plug this into
:
![y=-6x+b](https://tex.z-dn.net/?f=y%3D-6x%2Bb)
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
Recall that the y-intercept occurs when x=0. Given the point (0,2), we know that the y-intercept is 2. Plug this into
:
![y=-6x+2](https://tex.z-dn.net/?f=y%3D-6x%2B2)
I hope this helps!
Answer:
The vertex of the quadratic function is:
![(x_{v}, y_{v})=\left(-3,\:7\right)](https://tex.z-dn.net/?f=%28x_%7Bv%7D%2C%20y_%7Bv%7D%29%3D%5Cleft%28-3%2C%5C%3A7%5Cright%29)
Step-by-step explanation:
Given the function
![f\left(x\right)=x^2+6x+16](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3Dx%5E2%2B6x%2B16)
As the vertex of the form
is defined as:
![x_v=-\frac{b}{2a}](https://tex.z-dn.net/?f=x_v%3D-%5Cfrac%7Bb%7D%7B2a%7D)
As the quadratic function of parabola params are
![a=1,\:b=6,\:c=16](https://tex.z-dn.net/?f=a%3D1%2C%5C%3Ab%3D6%2C%5C%3Ac%3D16)
so
![x_v=-\frac{b}{2a}](https://tex.z-dn.net/?f=x_v%3D-%5Cfrac%7Bb%7D%7B2a%7D)
![x_v=-\frac{6}{2\cdot \:1}](https://tex.z-dn.net/?f=x_v%3D-%5Cfrac%7B6%7D%7B2%5Ccdot%20%5C%3A1%7D)
![x_v=-3](https://tex.z-dn.net/?f=x_v%3D-3)
Putting
to determine ![y_v](https://tex.z-dn.net/?f=y_v)
![y_v=\left(-3\right)^2+6\left(-3\right)+16](https://tex.z-dn.net/?f=y_v%3D%5Cleft%28-3%5Cright%29%5E2%2B6%5Cleft%28-3%5Cright%29%2B16)
![y_v=3^2-18+16](https://tex.z-dn.net/?f=y_v%3D3%5E2-18%2B16)
![y_v=9-2](https://tex.z-dn.net/?f=y_v%3D9-2)
![y_v=7](https://tex.z-dn.net/?f=y_v%3D7)
Therefore, the vertex of the quadratic function is:
![(x_{v}, y_{v})=\left(-3,\:7\right)](https://tex.z-dn.net/?f=%28x_%7Bv%7D%2C%20y_%7Bv%7D%29%3D%5Cleft%28-3%2C%5C%3A7%5Cright%29)