Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²

This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)

Latus rectum: y-value = 15/2

Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5

4 0

3 years ago

Evaluate the expression 10^2+(3+5)^2 - 5=

vampirchik [111]

Answer:

159

Step-by-step explanation:

10^2+(3+5)^2-5

-> 100 + (3+5)^2 -5

-> 100 + 8^2 - 5

-> 100 + 64 - 5

-> 159

8 0

2 years ago

Read 2 more answers

Which expression is equivalent to √-80? 4√5 -4√5 -4i √ 5 4i √ 5

miskamm [114]

Answer:

4i√5

Step-by-step explanation:

$\sqrt{-80}=\sqrt{(-1)(16)(5)}=\sqrt{-1}\cdot\sqrt{16}\cdot\sqrt{5}=4i\sqrt{5}$

6 0

3 years ago

C is the midpoint of BD. If BC = x + 7 and CD = 8x, what is CD?

Anastaziya [24]

Given :- 

C is the midpoint of BD .
BC = x + 7
CD = 8x

To Find :-

Value of BD ( correct )

Answer :- 

As C is the midpoint , we can say that the line is BCD . So that ,

BC + CD = BD

Substitute the values ,

( x+7 ) + 8x = BD
BD = x + 8x + 7
BD = 9x + 7 .

Hence the value of BD is 9x + 7 .

8 0

2 years ago