Question

Find the x-intercepts of the parabola with vertex (-7,45) and y-intercept (0,-200).
Write your answer in this form: (x1,y1),(x2,y2).
If necessary, round to the nearest hundredth.
Use the method of completing the square to write the equation of the given parabola in this form:

(y – k) = a(x – h)2
where a ≠ 0, (h,k) is the vertex, and x = h is the axis of symmetry.

Answer 1

please help

Answer 2

@THEHELPER123

Answer 3

@phi @dan815 @IrishBoy123 @pooja195 @welshfella

Answer 4

find the common denominator

Answer 5

wrong person

Answer 6

oh okay

Answer 7

i just dont understand this

Answer 8

did you learn the vertex form of an equation for a parabola?

Answer 9

i have notes....let me see

Answer 10

what it says

Answer 11

well its asking for me to complete the square

Answer 12

it confuses me though because they ask it in a different way

Answer 13

@jabez177

Answer 14

@AlexandervonHumboldt2

Answer 15

the form is
\[ y= a(x-h)^2 + k\]
where (h,k) is the vertex

they tell you the vertex, so you can replace the h and k with numbers in that formula
can you do that ?

Answer 16

ehhh yeh

Answer 17

there are 4 numbers though......

Answer 18

i cant put both h and k in can i? i mean both h and k's i cant

Answer 19

the vertex is (-7, 45)
that means use h=-7 and k= 45 in the equation
y = a(x-h)^2 + k

so replace the h and k letters with numbers.
what do you get ?

Answer 20

ohh okay let me try

Answer 21

y=a(x-7)^2+45?

Answer 22

it should be x - h
in this case x- (-7)

Answer 23

im really lost like this is algebra 2 and up. i only know algebra 1 or less.

Answer 24

can you fix your equation? it is not x-7

Answer 25

ehh y=a(-7)+45?

Answer 26

no, don't get lost.
you want a(x-h)^2 + 45
h is -7
can you simplify x - -7 ?
minus a minus is plus, remember?

Answer 27

yeah but im not a very mathematical person. all i see are letters ,numbers,and signs

Answer 28

and then my brain goes in 5 different ways

Answer 29

examples:
1 - 1 = 0
1- -1 = 1+1= 2

Answer 30

ohh

Answer 31

x- -7 is x+7

Answer 32

so far you have
\[ y= a(x+7)^2 + 45\]
they also tell you (0,-200) is on the curve

"plug in" x=0 and y= -200 into your equation.
what do you get ?

Answer 33

okay so let me do this

Answer 34

im working it out on paper

Answer 35

uhm is it -200=a(0+7)^2+45?

Answer 36

yes. now remember order of operations?
first do the parens: 0+7

Answer 37

yeah hold on

Answer 38

do i square the -7?

Answer 39

so that would be -200=a(-49)+45?

Answer 40

you get
-200= a(7)^2 + 45

(it's +7 or just 7)
but yes, now do 7*7

Answer 41

which is 49

Answer 42

yes
uhm is it -200=a(0+7)^2+45?
becomes
-200 = 49a + 45

now add -45 to both sides

Answer 43

like this
-200 + -45 = 49a + 45 + -45

Answer 44

oooh yeah okay hold on

Answer 45

is it a=-200/49?

Answer 46

go slower. you have the right idea, but you have to be careful

-200 + -45 = 49a + 45 + -45


on the left side, what is -200 + -45

Answer 47

-245

Answer 48

and on the right side 45 + -45 is 0
so you have
-245 = 49a + 0
adding 0 does not do anything so it's just
-245= 49a
or
49a = -245

Answer 49

now you can divide both sides by 49

Answer 50

so divide -245 by 49 and 49 by 49 which will be 1/5

Answer 51

i think...

Answer 52

you do
\[ \frac{49}{49} a = \frac{-245}{49} \]

Answer 53

yeah i did that so a=5?

Answer 54

you mean a= -5 , right ?

Answer 55

oh yeah lol

Answer 56

okay so i have to solve for x and y?

Answer 57

and one point is -5

Answer 58

you found a= -5 so the equation of the curve
\[ y= a(x+7)^2 + 45 \]
is
\[ y = -5(x+7)^2 +45\]
this equation tells us everything we want to know about the parabola.

Answer 59

oooh so i just plug it in now?

Answer 60

They want
Find the x-intercepts of the parabola

the x-intercepts are the x values when y is 0
in other words, we have to "solve for x" when y is 0:
\[ y = -5(x+7)^2 +45\\ -5(x+7)^2 +45=0\]
I would first add -45 to both sides

Answer 61

it depens what we are looking for like is it x

Answer 62

okay so its -7 then

Answer 63

no, when x is 0, we get the y-intercept.
this is harder. we set the y=0 and we have to find the x that makes y zero.
we start with
\[ -5(x+7)^2 +45 = 0\]
now add -45 to both sides

Answer 64

okay well -5+ -45 is 40

Answer 65

oops i mean -50

Answer 66

write down the entire equation (including the x stuff!)
\[ -5(x+7)^2 +45 + -45= 0+-45\]

Answer 67

okay

Answer 68

to review, we start with
\[ -5(x+7)^2 +45 = y\]
and we set y =0 (this is how to find the x-intercepts)
\[ -5(x+7)^2 +45 = 0\]
now we add -45 to both sides
\[ -5(x+7)^2 = -45 \]
next , divide both sides by -5

Answer 69

okay i got 1 and 9

Answer 70

you get
\[ (x+7)^2 = \frac{-45}{-5} \]

Answer 71

or
\[ (x+7)^2 = 9\]
now take the square root of both sides

Answer 72

square root of both sides?

Answer 73

yes. do you know how to do that ?

Answer 74

just 7^2 or 9^2

Answer 75

or what goes into both evenly

Answer 76

ugh i give up

Answer 77

square root "undoes" the square
in other words you do
\[ \sqrt{(x+7)^2} = \sqrt{9} \]

Answer 78

and it's worth remembering
\[ \sqrt{x^2} = x \]
or in this case
\[ \sqrt{(x+7)^2}= x+7\]

Answer 79

for the square root of 9, what number times itself is 9 ?
3*3 is 9
that means 3 is the square root.

or if you are confused, you can use a calculator
you get
\[ x+7= \pm 3 \]
we usually show both -3 and +3 work: -3*-3 is 9 and so is 3*3 = 9

Answer 80

we have two different equations:
x+7 = -3
and
x+7 = 3
solve each one.

can you do that ?

Answer 81

yeah

Answer 82

hold on