Question

Refresher..

Answer 1

Positive graph..
Vertex- (-1,0)

Answer 2

f(x)=(x-h)^2 +k
f(x)= a(x-(-1))^2 +0
= a(x+1)^2 +0

Answer 3

Not sure if I did that right so far..

Answer 4

yes. and to find a, use a point on the curve (but not the vertex)
for example (0,1)

Answer 5

1= a(0+1)^2
1 = a
so a is 1 and the equation is
y= (x+1)^2

or multiplied out
y= x^2 +2x+1

Answer 6

or you could test the point (-1,0) in each of the choices
that works for choices B and C
then use (0,1) to see C is the only equation that works

Answer 7

True.

Answer 8

another way:

use -b/(2a) to find the x value of the vertex
you want that to be -1
and only choice C works

Answer 9

Hmm never thought of that

Answer 10

the first two choices have b=0 so you get x=0. those are wrong.
choice C gives -2/2= -1 (that works)
choice D give s -(-2)/2= +1 (nope)

Answer 11

Okay.

Answer 12

Next problem..

Answer 13

Find the range of the quadratic function.

f(x)= x^2 -8x-5

Answer 14

parabola with \( \cup\) shape
so from the y value of the vertex to + infinity

Answer 15

Um do you mean -5 to infinity

Answer 16

Sorry I dont really remember how to solve this one.

Answer 17

range are the y values
it is U shaped, so you want the smallest y value (which happens at the vertex)

Answer 18

you find the x value of the vertex using -b/(2a)
and use that x value to find the corresponding y value. that will be the smallest y value on the curve.
and of course y will go to + infinity as you put in bigger and bigger x values

Answer 19

Okay thats what I thought

Answer 20

but the smallest y is not -5

Answer 21

Yeah sorry I was confused at first

Answer 22

Vertex- (4,-12)
Range- [-21, infinity)

Answer 23

yes, looks good

Answer 24

Okay

Answer 25

A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.

Answer 26

A= 18x -2x^2

Answer 27

x= -(-2) over 2(18) .... I think I need to change it to -2x^2 +18

Answer 28

Answer -> 4.5

Answer 29

A= 18x -2x^2
yes, but generally we write it in standard form
A= -2x^2 + 18x

this is a \(\cap\) shape, and its vertex has the biggest y value (in this case largest area)

Answer 30

x of vertex is -b/(2a)= -18/(2*-2) = 18/4 = 9/2 = 4.5
yes you found the correct answer:
d= 4.5 inches to maximizes the area of the cross-section

Answer 31

Okay thank you.