PLEASE HELP
A sketch of the graph y = 2x² - 4x – 7 is shown.
Find the values identified as a, b, c, d and e on the sketch.

Answer:

a = (0, -7)

b = (1, 0)

c = (-9, 0)

d = (1 - 3√2 / 2, 0)  ≈ (-1.1213, 0)

e = (1 + 3√2 / 2, 0) ≈ (3.1213, 0)

Step-by-step explanation:

----- points d and e ----

d and e we can find by solving for y = 0:

2x² - 4x - 7 = 0

2x² - 4x = 7

x² - 2x = 7/2

x² - 2x + 1 = 9/2

(x - 1)² = 9/2

x - 1 = √(9/2)

x = 1 ± 3√2 / 2

x ≈ 1 ± 2.1213

x ≈ 3.1213, -1.1213

So d is at approximately (-1.1213, 0), and e (3.1213, 0)

--- point a ---

Much easier to do, we simply need to solve for x = 0:

y = 2 × 0² - 4 × 0 - 7

y = -7

So point a is at (0, -7)

--- points b and c ---

We can find these in a couple of interesting ways. We've actually found b already, as it's halfway between points d and e.  You'll recall that those are calculated as 1 ± 3√2 / 2, meaning that the midway point between them is just 1.

An alternate way of doing it is to apply some basic calculus, finding the point at which the curve has a slope of zero, which will give us b's x coordinate:

y = 2x² - 4x - 7

dy/dx = 4x - 4

0 = 4x - 4

4x = 4

x = 1

So b is equal to (1, 0).

To find c, we simply plug that x = 1 into the original function:

y = 2x² - 4x - 7

y = 2(1)² - 4(1) - 7

y = 2 - 4 - 7

y = -9

so c lies on (0, -9)

a = (0, -7)

b = (1, 0)

c = (-9, 0)

d = (1 - 3√2 / 2, 0)  ≈ (-1.1213, 0)

e = (1 + 3√2 / 2, 0) ≈ (3.1213, 0)

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Given

----- points d and e ----

d and e we can find by solving for y = 0:

2x² - 4x - 7 = 0

2x² - 4x = 7

x² - 2x = 7/2

x² - 2x + 1 = 9/2

(x - 1)² = 9/2

x - 1 = √(9/2)

x = 1 ± 3√2 / 2

x ≈ 1 ± 2.1213

x ≈ 3.1213, -1.1213

So d is at approximately (-1.1213, 0), and e (3.1213, 0)

--- point a ---

Much easier to do, we simply need to solve for x = 0:

y = 2 × 0² - 4 × 0 - 7

y = -7

So point a is at (0, -7)

--- points b and c ---

We can find these in a couple of interesting ways. We've actually found b already, as it's halfway between points d and e.  You'll recall that those are calculated as 1 ± 3√2 / 2, meaning that the midway point between them is just 1.

An alternate way of doing it is to apply some basic calculus, finding the point at which the curve has a slope of zero, which will give us b's x coordinate:

y = 2x² - 4x - 7

dy/dx = 4x - 4

0 = 4x - 4

4x = 4

x = 1

So b is equal to (1, 0).

To find c, we simply plug that x = 1 into the original function:

y = 2x² - 4x - 7

y = 2(1)² - 4(1) - 7

y = 2 - 4 - 7

y = -9

so c lies on (0, -9)

To learn more about co-ordinate geometry refer to:

https://brainly.com/textbook-solutions/q-use-figure-shown-exercises-14-17-example-14

#SPJ2

Help me plzz its due TODAYYYY

Sara's office recycled a total of 12 pounds of paper over 4 weeks. How many weeks will it take Sara's office to recycle a total of 48 pounds of paper?

On a parabola, the extreme point (which is the highest, lowest, or farthest
point left or right) is called the
A. focus
B. vertex
C. directrix
D. center

Please help! Image attached ;'(

Brian started with $300 in savings account. After 5 years he earned $18 in interest. What is the simple interest rate on his account?

WILL GIVE BRAINLIEST

bxvy - xvyb

if b=-2
x= 1
y= -1
v= 3

simplify and substitute

There were 128 children signed up for baseball camp. If each team is made up of 12
children, how many teams will there be and how many children are left over?

Help please... I need help on this , this is 8th grade math

Which number has only two factors?

A: 6
B: 8
C: 9
D: 11​

Because a Rectangle is a parallelogram the properties that were true for a parallelogram are also true for a rectangle. TRUE OR FALSE ?

Is this right?
R is the midpoint of QT

Which ratio forms a proportion with 7/4?

A. 49
B.1512
C. 25
D. 36

My question is what is 69 x 420?










Once upon a time, there was a lovely princess. But she had an enchantment upon her of a fearful sort, which could only be broken by love's first kiss. She was locked away in a castle, guarded by a terrible fire-breathing dragon. Many brave knights had attempted to free her from the dreadful prison, but none prevailed. She waited in the dragon's keep, in the highest room of the tallest tower, for her true love and true love's first kiss." [Laughing] Like that's ever gonna happen.
[Paper Rustling, Toilet Flushes]
Shrek: What a load of--
[Toilet Door slams]
Shrek hops out his outhouse and his routine like taking a mud shower and farting in his pool.
[♪ All-Star By Smash Mouth Playing]
Steve Harwell: ♪ Somebody once told me the world is gonna roll me, I ain't the sharpest tool in the shed. She was lookin' kind of du mb with her finger and her thumb in the shape of an "L" on her forehead. The years start comin', and they don't stop comin', fed to the rules and I hit the ground runnin', didn't make sense not to live for fun. Your brain gets smart but your head gets du mb. So much to do, so much to see, so what's wrong with takin' the backstreets. You'll never know if you don't go, you'll never shine if you don't glow. Hey, now, you're an all-star. Get your game on, go play. Hey, now, you're a rock star. Get the show on, get paid. And all that glitters is gold, only shootin' stars break the mold. It's a cool place, and they say it gets colder, you're bundled up now, but wait till you get older. But the meteor men beg to differ judging by the hole in the satellite picture. The ice we skate is gettin' pretty thin, the water's getting warm so you might as well swim. My world's on fire, how 'bout yours? That's the way I like it and I'll never get bored. Hey, now, you're an all-star. ♪
[Shouting]
Steve Harwell: ♪ Get your game on, go play. Hey, now, you're a rock star. Get the show on, get paid. And all that glitters is gold, only shootin' stars break the mold. ♪
[Belches]
Villagers: Go! Go!
[Record Scrating]
Steve Harwell: ♪ Go. Go. Go. Hey, now, you're an all-star. Get your game on, go play. Hey, now, you're a rock star, get the show on, get paid. And all that glitters is gold, only shootin' stars break the mold. ♪
Villagers: Think it's in there? All right! Let's get it!
Villager 1: Whoa. Hold on. Do you know what that thing could do to you?
Villager 2: Yeah, it'll grind your bones for its bread.
Shrek: [Laughs] Yes, well, actually, that would be a giant. Now, ogres-- they're much worse. They'll make a suit from your freshly peeled skin.
Villager 3: No!
Shrek: They'll shave your liver. Squeeze the jelly from your eyes! Actually, it's quite good on toast.
Villager 3: Back! Back, beast! Back! I warn ya!
[Gasping]
Villager 3: Right.
[Roaring]
[Shouting]
[Roaring]
[Roaring Continues]
[Shouting Continues]
Shrek: [Whispers] This is the part where you run away.
[Gasping]
Shrek: [Laughs] [Laughing] And stay out! "Wanted. Fairy tale creatures." [Sighs]
Guard 1: All right. This one's full. Take it away!
[Gasps]
Guard 2: Move it along. Come on! Get up!
Captain of the Guards: Next!
Guard 3: Give me that! Your flying days are over.
Captain of the Guards: That's 20 pieces of silver for the witch. Next!
Guard 4: Get up!
Captain of the Guards: Twenty pieces.
Guard 5: Come on!
[Thudding]
Guard 6: Sit down there! Keep quiet!
Bear: [Crying] This cage is too small.

Why does this gotta be 20-

what's the answer for this equation?
-2(5x+1)=58+10x

Help!!!!!! Math problems

A car is moving along Highway 138 according to the given equation, where x meters is the directed distance of the car from a given point P at t hours. Find the values of t for which the acceleration is zero, and then find the position of the car at this time.

x = 1/4t^3 + 1/6t^3 - t^2+ 1

enter the lengths of QS and TV

QS=
TV=​

-30n - 10
Please answer

y = 1x1
2x + 1y = 4


Y=1x-3
4x+1y=32

malik buys and sells car parts. he bought two tires for 45.00$

Identify the vertex and
the axis of symmetry of the parabola. Identify points corresponding to P and Q.



PLS HELP TAKIN TEST RN MARKING BRANLIST

I need help lol please

Write an equation in point slope form of a line passing through 3,6 having a slope of 1/3

I NEED HELP ASAP!!!!!!

help plssssssssssssssss

which expression best represents the phrase"7 less than the quotient of 2x and 5"

Plsssss help!!!!! I’m rewarded a lot of points.

Denna has 80 books in her collection now. If 60% of the books are fiction,how many of the books are nonfiction?

A triangle has sides with eng sof 4 meters, 5 meters, and 7 meters.
Is it a right triangle?