Answer:
Answer c): write the function in standard form
Step-by-step explanation:
To start with, it is important to write the polynomial in standard form, so as to have the two terms with the dependence in x together:
![6x^2-42\,x+5](https://tex.z-dn.net/?f=6x%5E2-42%5C%2Cx%2B5)
then you extract 6 as a common factor of just the terms with the variable x:
![6(x^2-7x)+5](https://tex.z-dn.net/?f=6%28x%5E2-7x%29%2B5)
Then proceed to complete the square in the expression inside the parenthesis:
![6(x^2-7x+\frac{49}{4} -\frac{49}{4})+5](https://tex.z-dn.net/?f=6%28x%5E2-7x%2B%5Cfrac%7B49%7D%7B4%7D%20-%5Cfrac%7B49%7D%7B4%7D%29%2B5)
![6\,((x-\frac{7}{2} )^2-\frac{49}{4} )+5\\6\,(x-\frac{7}{2} )^2-\frac{147}{2}+5\\6\,(x-\frac{7}{2} )^2-\frac{137}{2}](https://tex.z-dn.net/?f=6%5C%2C%28%28x-%5Cfrac%7B7%7D%7B2%7D%20%29%5E2-%5Cfrac%7B49%7D%7B4%7D%20%29%2B5%5C%5C6%5C%2C%28x-%5Cfrac%7B7%7D%7B2%7D%20%29%5E2-%5Cfrac%7B147%7D%7B2%7D%2B5%5C%5C6%5C%2C%28x-%5Cfrac%7B7%7D%7B2%7D%20%29%5E2-%5Cfrac%7B137%7D%7B2%7D)
Then, the function can be finally be written as:
![f(x)=6\,(x-\frac{7}{2} )^2-\frac{137}{2}](https://tex.z-dn.net/?f=f%28x%29%3D6%5C%2C%28x-%5Cfrac%7B7%7D%7B2%7D%20%29%5E2-%5Cfrac%7B137%7D%7B2%7D)
in vertex form
Answer:
same lol
Step-by-step explanation:
We know that
center (−1, 4) and <span>passes through the point (3, −5)
</span><span>the value for the radius is,
using the Distance Formula---------r=</span>√(4+5)²+(-1-3)²=√(9²+(-4)²
r=√97
<span>equation for a standard form for a circle
(x-h)</span>²+(y-k)²=r²
<span>the center is (h,k)-----------> (-1,4)
</span>(x+1)²+(y-4)²=(√97)²---------------> (x+1)²+(y-4)²=97
the answer is
(x+1)²+(y-4)²=97
9514 1404 393
Answer:
- parallel: y = 4x -6
- perpendicular: y = -1/4x +27/4
Step-by-step explanation:
If we want the new line to be written in slope-intercept form, we need to find the new value of the y-intercept. The equation of the line is ...
y = mx +b . . . . . . . for slope m and y-intercept b
Solving for b gives ...
b = y -mx . . . . . . . subtract mx from both sides.
The values of x and y come from the point we want the line to pass through. The value of m will be the same for the parallel line as for the given line: 4. For the perpendicular line, it will be the opposite reciprocal of this: -1/4.
<u>Parallel line</u>
b = 6 -4(3) = 6 -12 = -6
y = 4x -6
Perpendicular line
b = 6 -(-1/4)(3) = 6 +3/4 = 27/4
y = -1/4x +27/4