Answer:
A) coressponding ; Vertical
Answer:
y = -8x + 3
Step-by-step explanation:
plug in the point and the slope into the slope intercept formula (y=mx+b)
the slope will be the same since you want the line to be parallel
11 = -8(-1) +b now solve for b
11 = 8 + b
-8 -8
3 = b
now write the equation with only the slope and the y intercept
y = -8x + 3
The function in vertex form is
⇒ 3rd answer
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
- a is the coefficient of x²
- (h , k) are the coordinates of the vertex point
, wher b is the coefficient of x- k = f(h), that means value f(x) when x = h
∵ f(x) = x² + x + 1
∴ a = 1 , b = 1
∵ ![h=\frac{-b}{2a}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-b%7D%7B2a%7D)
- Substitute the values of a and b to find h
∴ ![h=\frac{-1}{2(1)}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-1%7D%7B2%281%29%7D)
∴ ![h=\frac{-1}{2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-1%7D%7B2%7D)
Substitute the value of x in f(x) by the value of h to find k
∵ f(
) = ![(\frac{-1}{2})^{2}+\frac{-1}{2}+1](https://tex.z-dn.net/?f=%28%5Cfrac%7B-1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B-1%7D%7B2%7D%2B1)
∴ f(
) = ![\frac{1}{4}-\frac{1}{2}+1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B1%7D%7B2%7D%2B1)
∴ f(
) = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
- k is the value of f(x) when x = h
∵ h = ![\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7D)
∴ k = f(
)
∴ k = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
Substitute the values of a, h and k in the vertex form
∵ f(x) = a(x - h)² + k
∵ a = 1 ,
, ![k=\frac{3}{4}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B3%7D%7B4%7D)
∴ ![f(x)=1(x-\frac{-1}{2})^{2}+\frac{3}{4}](https://tex.z-dn.net/?f=f%28x%29%3D1%28x-%5Cfrac%7B-1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D)
∴ ![f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D)
The function in vertex form is ![f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D)
Learn more:
You can learn more about the quadratic functions in brainly.com/question/9390381
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