Question

Suppose a parabola has vertex (5, –3) and also passes through the point (6, 1). Write the equation of the parabola in vertex form.
y = (x – 5)2 – 3
y = 4(x – 5)2 – 3
y = 4(x + 5)2 – 3
y = 4(x – 5)2 + 3

Answer 1

ok if the vertex is \((5,-3)\) then it looks like
\[y=a(x-5)^2-3\]

Answer 2

then to find out which one it is, you know if \(x=6\) then \(y=1\) because that is what "passes through the point \((6,1)\) means
replace \(x\) by \(6\) and set the result equal to \(1\)

Answer 3

you get \[1=a(6-5)^2-3\]
\[1=a-3\]
\[4=a\]

Answer 4

pick
\[y = 4(x – 5)^2 – 3\]

Answer 5

thanks

Answer 6

yw

Answer 7

can you help with more?

Answer 8

sure

Answer 9

identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)2 – 3. (1 point)
vertex: (2, –3); axis of symmetry: x = 2
vertex: (–2, –3); axis of symmetry: x = –2
vertex: (2, 3); axis of symmetry: x = 2
vertex: (–2, 3); axis of symmetry: x = –2

Answer 10

\[y=3(x+2)^2-3\] read off from \(y=a(x-h)^2+k\) with vertex \((h,k)\) and axis of symmetry \(x=h\)

Answer 11

Identify the maximum or minimum value and the domain and range of the graph of the function y = 2(x – 3)2 – 4. (1 point)
minimum value: –4
domain: all real numbers
range: all real numbers –4
maximum value: 4
domain: all real numbers
range: all real numbers 4
maximum value: –4
domain: all real numbers –4
range: all real numbers
minimum value: 4
domain: all real numbers4
range: all real numbers

Answer 12

in your case \(h=-2\) and \(k=-3\) so vertex is \((-2,-3)\) and axis of symmetry is \(x=-2\)

Answer 13

that was for the second question you posted

Answer 14

third question
Identify the maximum or minimum value and the domain and range of the graph of the function \(y = 2(x – 3)^2 – 4\)

Answer 15

this is a parabola that opens up, so it has a minimum, not a maximum. the minimum is the second coordinate of the vertex, which is \(-4\) so the range is from \(-4\) to \(\infty\) or "all real numbers greater than or equal to \(-4\)

Answer 16

\(-4\) is the minimum
the domain of any polynomial is all real numbers

Answer 17

i don't really understand your choices, but if the first one is

minimum value: –4
domain: all real numbers
range: all real numbers \(\geq –4\)

then it is the right one

Answer 18

thanks

Answer 19

The graph below models the path of a golf ball after it was hit. Write an equation in vertex form that represents the path of the ball.
y = –(x – 50)2 + 150
y = –(x – 150)2 + 50
y = –(x – 100)2 + 150
y = –(x – 50)2 + 150

Answer 20

last one @satellite73

Answer 21

lol

Answer 22

my eyes aren't that good, but i looks like the vertex is \((50,150)\) is that right ?

Answer 23

i cant see it either :/

Answer 24

if so it is \[y=-(x-50)^2+150\] it looks like you posted that answer twice, first and last

Answer 25

looks like the top of the parabola is where \(x=50\) and \(y=150\)

Answer 26

thanks .. Your the bestXD

Answer 27

go with
\[y=-(x-50)^2+150\] first answer and also the last, unless that was a typo

Answer 28

happy to help. zombies rule

Answer 29

do you know what your grade was on this?

Answer 30

@ZombieGirl

Answer 31

oןןǝɥ