Z= F+ (g/n) (you’re welcome)
Answer:
a. Vertex = (2.5,-12.25)
b. y-intercept = (0,-6)
c. x-intercept = (6,0) ; (-1,0)
Step-by-step explanation:
a.
Your equation is written as:
![y = ax^{2} + bx +c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E%7B2%7D%20%2B%20bx%20%2Bc)
The easiest way to find the vertex is writing the equation this way:
![y = a(x-h)^{2}+k](https://tex.z-dn.net/?f=y%20%3D%20a%28x-h%29%5E%7B2%7D%2Bk)
Being the vertex (h,k)
So first complete the square
![y = x^{2} -5x -6 \\y = x^{2} - 2(2.5x) -6 \\y = x^{2} - 2(2.5x) +2.5^{2} - 2.5^{2} -6 \\y = (x^{2} -2(2.5x) + 2.5^{2}) -6.25 - 6 \\y = (x-2.5)^{2} -12.25](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D%20-5x%20-6%20%5C%5Cy%20%3D%20x%5E%7B2%7D%20-%202%282.5x%29%20-6%20%5C%5Cy%20%3D%20x%5E%7B2%7D%20-%202%282.5x%29%20%2B2.5%5E%7B2%7D%20-%202.5%5E%7B2%7D%20-6%20%5C%5Cy%20%3D%20%28x%5E%7B2%7D%20-2%282.5x%29%20%2B%202.5%5E%7B2%7D%29%20-6.25%20-%206%20%5C%5Cy%20%3D%20%28x-2.5%29%5E%7B2%7D%20-12.25)
Vertex : (2.5,-12.25)
b.
To find the y-intercept you need to replace the equation when x = 0 and get y
![y = (0)^{2} - 5(0) -6\\y = - 6](https://tex.z-dn.net/?f=y%20%3D%20%280%29%5E%7B2%7D%20-%205%280%29%20-6%5C%5Cy%20%3D%20-%206)
c.
To find the x-intercept you need to replace the equation when y = 0 and get x
![0 = x^{2} - 5x -6 \\0 = (x-6)(x+1)\\x = 6\\x = -1](https://tex.z-dn.net/?f=0%20%3D%20x%5E%7B2%7D%20-%205x%20-6%20%5C%5C0%20%3D%20%28x-6%29%28x%2B1%29%5C%5Cx%20%3D%206%5C%5Cx%20%3D%20-1)
Answer:
2
Step-by-step explanation:
If p = 5 and q = 1, the equation would look like
2 - (1 - 5/5)
2 - (1 - 1) [5/5 is a giant 1]
2 - (0)
2
M= 6 so 2m would be 12 and 12-3=9
Answer:
x = 3.873 units
or x =
units
Step-by-step explanation:
Hypotenuse = 4 , x = height of this isosceles triangle.
base is 2,
so Use Pythagorean Theorem.
x^2 + 1^2 = 4^2
x^2 = 4^2 - 1^2
x^2 = 16 - 1 = 15
x = root(15) =