1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Firdavs [7]
3 years ago
5

Identify the vertex and the y-intercept of the graph of each function. Show your work

Mathematics
1 answer:
olga2289 [7]3 years ago
6 0
<u>vertex</u>
y = 3(x - 2)² - 4
y = 3((x - 2)(x - 2)) - 4
y = 3(x² - 2x - 2x + 4) - 4
y = 3(x² - 4x + 4) - 4
y = 3(x²) - 3(4x) + 3(4) - 4
y = 3x² - 12x + 12 - 4
y = 3x² - 12x + 8
3x² - 12x + 8 = 0
x = <u>-(-12) +/- √((-12)² - 4(3)(8))</u>
                       2(3)
x = <u>12 +/- √(144 - 96)</u>
                   6
x = <u>12 +/- √(48)
</u>              <u> </u> 6<u>
</u>x =<u> 12 +/- 6.93</u>
 <u />             6
x = 2 +/- 1.155
x = 2 + 1.155      x = 2 - 1.155
x = 3.155            x = 0.845
y = 3x² - 12x + 8
y = 3(3.155)² - 12(3.155) + 8
y = 3(1.334025) - 3.786 + 8
y = 4.002075 - 3.786 + 8
y = 0.216075 + 8
y = 8.216075
(x, y) = (3.155, 8.216075)
or
y = 3x² - 12x + 8
y = 3(0.845)² - 12(0.845) + 8
y = 3(0.714025) - 10.14 + 8
y = 2.142075 - 10.14 + 8
y = -7.857925 + 8
y = 0.142675
(x, y) = (0.845, 0.142675)
<u>y-intercept</u>
y = 3x² - 12x + 8
y = 3(0)² - 12(0) + 8
y = 3(0) - 0 + 8
y = 0 - 0 + 8
y = 0 + 8
0 = -y + 8
y = 8
(x, y) = (0, 8)
-------------------------------------------------------------------------------------------
<u>vertex</u>
y = 4(x - 5)² = 1
y = 4(x - 5)² - 1
y = 4((x - 5)(x - 5)) - 1
y = 4(x² - 5x - 5x + 25) - 1
y = 4(x² - 10x + 25) - 1
y = 4(x²) - 4(10x) + 4(25) - 1
y = 4x² - 40x + 100 - 1
y = 4x² - 40x + 99
4x² - 40x + 99 = 0
x = <u>-(-40) +/- √((-40)² - 4(4)(99))</u>
                         2(4)
x = <u>40 +/- √(1600 - 1584)</u>
                     8
x = <u>40 +/- √(16)</u>
              8
x = <u>40 +/- 4</u>
            8
x = 5 +/- 1/2
x = 5 + 1/2      x = 5 - 1/2
x = 5 1/2         x = 4 1/2
y = 4x² - 40x + 99
y = 4(5 1/2)² - 40(5 1/2) + 99
y = 4(30 1/4) - 220 + 99
y = 121 - 220 + 99
y = -99 + 99
y = 0
(x, y) = (5 1/2, 0)
or
y = 4x² - 40x + 99
y = 4(4 1/2)² - 40(4 1/2) + 99
y = 4(20 1/4) - 180 + 99
y = 81 - 180 + 99
y = -99 + 99
y = 0
(x, y) = (4 1/2, 0)
<u>y-intercept</u>
y = 4x² - 40x + 99
y = 4(0)² - 40(0) + 99
y = 4(0) - 0 + 99
y = 0 - 0 + 99
y = 0 + 99
y = 99
(x, y) = (0, 99)
--------------------------------------------------------------------------------------------
<u>vertex</u>
y = (x - 1)² = 2
y = (x - 1)² - 2
y = ((x - 1)(x - 1)) - 2
y = (x² - x - x + 1) - 2
y = x² - 2x + 1 - 2
y = x² - 2x - 1
x² - 2x - 1 = 0
x = <u>-(-2) +/- √((-2)² - 4(1)(-1))</u>
                     2(1)
x = <u>2 +/- √(4 + 4)</u>
                2
x = <u>2 +/- √(8)</u>
             2
x = <u>2 +/- 2.83</u>
             2
x = 1 +/- 1.415
x = 1 + 1.415    x = 1 - 1.415
x = 2.415          x = 0.415
y = x² - 2x - 1
y = (2.145)² - 2(2.145) - 1
y = 4.60125 - 4.029 - 1
y = 0.57225 - 1
y = 0.42775
(x, y) = (2.415, 0.42775)
or
y = x² - 2x - 1
y = (0.415)² - 2(0.415) - 1
y = 0.172225 - 0.83 - 1
y = -0.657775 - 1
y = -1.657775
(x, y) = (0.415, -1.657775)
<u>y-intercept</u>
y = x² - 2x - 1
y = (0)² - 2(0) - 1
y = 0 - 0 - 1
y = 0 - 1
y = -1
(x, y) = (0, -1)
You might be interested in
Someone help me asap pleaseee!!
gogolik [260]

Answer:

B is correct.

6 0
2 years ago
Martin's class has 28 students in it 25 % of those students are homesick today. How many students are home sick
lisov135 [29]
7 students are home sick
7 0
2 years ago
The lines below are perpendicular. If
RSB [31]

Answer:

Correct answer: s₁ = - 2

Step-by-step explanation:

The relationship between the slope of two lines that are perpendicular is:

s₁ = - 1/s = - 1/(1/2) = - 2

God is with you!!!

5 0
3 years ago
Solve for a.
FinnZ [79.3K]

Answer:

iii) a=3b/2

Step-by-step explanation:

7a-2b= 5a+b

7a-5a=2b+b

2a=3b

a=3b/2

8 0
3 years ago
Read 2 more answers
5/4 × 9/10 <br>fraction in simplest form​
MaRussiya [10]

Answer:

\frac{9}{8}

Step-by-step explanation:

\frac{5}{4} \times \frac{9}{10} \\\\=\frac{5\times 9}{4\times 10}\\\\=\frac{1\times 9}{4\times 2}\\\\=\frac{9}{8}\\\\

3 0
3 years ago
Read 2 more answers
Other questions:
  • Please help! important!! worth 30 points
    8·2 answers
  • Which unit should be used to measure mass of pencil?
    13·2 answers
  • Charles rode 15 miles on his bicycle in 2.5 hours . barb rode her bicycle 8 miles in 1.5 hours at what rate fid Charles ride,in
    11·1 answer
  • A car with a mass of 1,250 kg travels at 2.24 m/s and bumps into a stopped car with a mass of 1,300 kg. After the collision, the
    12·1 answer
  • 3(4x + 2)<br> Pleaseee helppppp meeeeeee
    15·1 answer
  • How many times greater is the 7 in the ten thousands place than the 7 in the hundreds place in this number 74,731
    8·2 answers
  • Si una bolsa de plástico pesa cuatro kilogramos y contiene tres latas con atún y dos de mermelada, y en otra bolsa contiene dos
    13·1 answer
  • Tell whether the equation has one, zero, or infinitely many solutions.<br> 8(x-4) + 19 = 8x - 13
    8·1 answer
  • (LOTS OF POINTS MARK BRAINlEST) due today please help me !!!!! Don’t take long
    8·1 answer
  • A quantity with an initial value of 850 grows continuously at a rate of 90% per
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!