Answer:
A slope..... I can't do math
Step-by-step explanation:
Answer:
picture is too blurrllyty
Step-by-step explanation:
04rr
Chewing is freee wdymmm???
we have
![f(x)=\frac{1}{4} x^{2} +bx+10](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%20x%5E%7B2%7D%20%2Bbx%2B10)
This is a vertical parabola open upward
The axis of symmetry is equal to the x-coordinate of the vertex
The vertex is the point (h,k)
the equation of the axis of symmetry is ![x=h](https://tex.z-dn.net/?f=x%3Dh)
In this problem
![x=6](https://tex.z-dn.net/?f=x%3D6)
so the x-coordinate of the vertex is ![h=6](https://tex.z-dn.net/?f=h%3D6)
<u>Convert the quadratic equation in vertex form</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![f(x)-10=\frac{1}{4} x^{2} +bx](https://tex.z-dn.net/?f=f%28x%29-10%3D%5Cfrac%7B1%7D%7B4%7D%20x%5E%7B2%7D%20%2Bbx)
Factor the leading coefficient
![f(x)-10=\frac{1}{4}(x^{2} +4bx)](https://tex.z-dn.net/?f=f%28x%29-10%3D%5Cfrac%7B1%7D%7B4%7D%28x%5E%7B2%7D%20%2B4bx%29)
Complete the square. Remember to balance the equation by adding the same constants to each side
![f(x)-10+b^{2}=\frac{1}{4}(x^{2} +4bx+4b^{2})](https://tex.z-dn.net/?f=f%28x%29-10%2Bb%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B4%7D%28x%5E%7B2%7D%20%2B4bx%2B4b%5E%7B2%7D%29)
Rewrite as perfect squares
![f(x)+(b^{2}-10)=\frac{1}{4}(x+2b)^{2}](https://tex.z-dn.net/?f=f%28x%29%2B%28b%5E%7B2%7D-10%29%3D%5Cfrac%7B1%7D%7B4%7D%28x%2B2b%29%5E%7B2%7D)
![f(x)=\frac{1}{4}(x+2b)^{2}-(b^{2}-10)](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%28x%2B2b%29%5E%7B2%7D-%28b%5E%7B2%7D-10%29)
remember that
![h=6](https://tex.z-dn.net/?f=h%3D6)
so
![(x+2b)=(x-6)](https://tex.z-dn.net/?f=%28x%2B2b%29%3D%28x-6%29)
![2b=-6](https://tex.z-dn.net/?f=2b%3D-6)
![b=-3](https://tex.z-dn.net/?f=b%3D-3)
substitute in the equation
![f(x)=\frac{1}{4}(x-6)^{2}-((-3)^{2}-10)](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%28x-6%29%5E%7B2%7D-%28%28-3%29%5E%7B2%7D-10%29)
![f(x)=\frac{1}{4}(x-6)^{2}+1](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%28x-6%29%5E%7B2%7D%2B1)
therefore
<u>the answer is</u>
![b=-3](https://tex.z-dn.net/?f=b%3D-3)
I'm not sure if I got the second answer correct because I don't think I know it. but I hope this helped. :)