transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts.

Answers

Answer 1

Answer: $The\ vertex\ form\ of\ y=ax^2+bx+c:y=a(x-h)^2+k\n\nwhere\ h=(-b)/(2a)\ and\ k=f(h)=(-(b^2-4ac))/(4a)\n-----------------------------\n\ny=-2x^2-12x-10\n\na=-2;\ b=-12;\ c=-10\n\nh=(-(-12))/(2(-2))=(12)/(-4)=-3\n\nk=f(-3)=-2(-3)^2-12(-3)-10=-2\cdot9+36-10=-18+26=8\n\ntherefore:y=-2(x-(-3))^2+8\to\boxed{y=-2(x+3)^2+8}\leftarrow The\ vertex\ form$

$y-intercept\to f(0)=-2(0^2)-12(0)-10=\boxed{-10}\leftarrow y-intercept$

$x-intercept\ if\ y=0\n\n-2x^2-12x-10=0\ \ \ \ \ |divide\ both\ sides\ by\ (-2)\nx^2+6x+5=0\nx^2+x+5x+5=0\nx(x+1)+5(x+1)=0\n(x+1)(x+5)=0\iff x+1=0\ or\ x+5=0\n\n\boxed{x=-1\ or\ x=-5}\leftarrow x-intercept$

Answer 2

Answer: y=-2x^2-12x-10
to find the x value of the vertex find the axis of symmetry which is
-b/2a
=12/2(-2)
=-3
to find the y value of the vertex sub the axis of symmetry back into the original equation.
y=-2(-3)^2-12(-3)-10
y=8
vertex=(-3,8)
to put it into vertex form use y=a(x-h)^2 +k where h and k are the x and y values of the vertex respectively.

y=-2(x--3)^2 +8
y=-2(x+3)^2+8

to find the x intercept let y=0

-2x^2-12x-10=0
x^2+6x+5=0
use quad formula and you will get
x=-5 and -1

to find the y intercept let x=0

y= -2(0)^2-12(0)-10
y=-10

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Find the equation of the line through the point (2, 5) that cuts off the least area from the first quadrant. Give your answer using the form below.

Can someone please help me :(

Answers

Answer:

5 ≤ x

x ≥ 5

Step-by-step explanation:

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There are 8 students in a small class. To make a team, the names of the 2 of them will be drawn from a hat. How many different teams of 2 students are

Answers

use slot method
2 slots

8 choices for first slot
7 choices for second (since 1 is in 1st slot)
8 times 7=56

56 ways to make 2 person teams

The first name can be any one of the 8.
   For each of those . . .
The second name can be any one of the remaining 7.

Total number of ways that 2 names can be drawn = (8 x 7) = 56 .

But . . .

Each team can be drawn in two different ways . . .
   -- Smith first, then Cohen
   -- Cohen first, then Smith.

So, among the 56 ways to draw 2 names, you will find
each possible pair of names drawn twice, in the opposite
order.

The number of different 2-member teams is (56 / 2) = 28 .

Write the resultant of the two vectors as an ordered pair. <3, 6> and <5, –5>