The general equation is y-k=a(x-h)² where (h,k) is the vertex.
So in this case we have y+12=a(x+6)².
Plug in x=0, y=-24: -12=36a, and a=-⅓. Therefore y+12=-⅓(x+6)².
Answer:
Step-by-step explanation:
<u>Quadratic Function</u>
Standard Form of Quadratic Function
The standard representation of a quadratic function is:
where a,b, and c are constants.
When the zeros of f (x1 and x2) are given, it can be written as:
f(x)=a(x-x1)(x-x2)
Where a is a constant called the leading coefficient.
We are given the two roots of f: x1=-3 and x2=4, thus:
f(x)=a(x+3)(x-4)
We also know that f(5)=8, thus:
f(5)=a(5+3)(5-4)=8
Operating:
a(8)(1)=8
Solving:
a=1
The function is:
f(x)=1(x+3)(x-4)
Operating:
9514 1404 393
Answer:
i) ∠AOB = 87°
ii) ∠BOC = 72°
iii) ∠COD = 123°
iv) ∠AOD = 78°
Step-by-step explanation:
The first three angle measures can be read from the diagram. Find the rays that define the angle, and read the measure of the arc between them.
The last angle, AOD, is found using the fact that the sum of all of the angles around a point is 360°.
87° +72° +123° +∠AOD = 360°
∠AOD = 360° -282° . . . . . . . . . . subtract 282° from both sides
∠AOD = 78°
Answer:
Exact length = 2*sqrt(137) cm
Approximate length = 23.409 cm
====================================================
Work Shown:
Use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 22^2 = c^2
64 + 484 = c^2
548 = c^2
c^2 = 548
c = sqrt(548)
c = sqrt(4*137)
c = sqrt(4)*sqrt(137) ..... use the rule sqrt(x*y) = sqrt(x)*sqrt(y)
c = 2*sqrt(137) .... this is the exact length
c = 23.4093998214392 ... use your calculator to find the approximate length
c = 23.409
I rounded to three decimal places, but feel free to round however you want. Or be sure to follow any rounding instructions your teacher provides.
Answer:
1. x= 5, x=1
2. x= -4, x=2
3. x= -6, x=7
4. x= -7, x=5
5. x= -9, x=0
Step-by-step explanation:
<em>You do the X factoring-</em>
1.
A B C
x²+6x+5
(A)(C) and B
(1)(5)=5 6
Then figure out what two numbers multiply to get 5
but also add to 6. In this case, it would be 5 and 1
5x1= 5 and 5+1= 6
so it is:
x= 5, x= 1
Hope this helps!
