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
Citrus2011 [14]
2 years ago
11

Find the vertex of the given quadratic function.

Mathematics
1 answer:
AleksandrR [38]2 years ago
8 0

Answer: Choice B. The vertex is (6,-4)

=======================================================

Work Shown:

Step 1 is to expand out (x-8)(x-4) using the FOIL rule or the box method or the distribution rule

(x-8)(x-4) = x(x-4)-8(x-4)

(x-8)(x-4) = x*x+x*(-4)-8*x-8*(-4)

(x-8)(x-4) = x^2-4x-8x+32

(x-8)(x-4) = x^2-12x+32

So (x-8)(x-4) turns into x^2-12x+32

x^2-12x+32 is the same as 1x^2+(-12x)+32 which is in the form ax^2+bx+c. We see that a = 1, b = -12, c = 32

-----------------

Use the values of a & b to find the value of h, which is the x coordinate of the vertex

h = -b/(2*a)

h = -(-12)/(2*1)

h = 12/2

h = 6

Then this is plugged back into the original function to find the y coordinate of the vertex. We can use either (x-8)(x-4) or x^2-12x+32 since they are equivalent expressions

k = y coordinate of vertex

k = f(h) = f(6) since h = 6

f(x) = (x-8)(x-4)

f(6) = (6-8)(6-4)

f(6) = (-2)(2)

f(6) = -4

note that

f(x) = x^2-12x+32

f(6) = (6)^2-12(6)+32

f(6) = 36-72+32

f(6) = -36+32

f(6) = -4

So we get the same result using either expression

So k = f(h) = f(6) = -4

Since h = 6 and k = -4, the vertex is (h,k) = (6,-4). So that's why the answer is choice B.

You might be interested in
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 99 people
sertanlavr [38]

Answer:

The probability of getting someone in the 18-21 age bracket or someone who agreed to respond = 0.365

Step-by-step explanation:

The counts are as follows  

Age Group  No of people contacted No of refusals      Total  

18-21               88                                  8                       96

22-29              240                                  42                       282

Total              328                                  50                       378

 

The probability of getting some one in the age bracket of 18-21 or some one who refused to respond is

= \frac{96}{378} + \frac{50}{378} - \frac{8}{378} \\= \frac{96+50-8}{378} \\= \frac{138}{378} \\= 0.365

8 0
3 years ago
Which is greater, 4 tenths and 2 hundredths or 2 tenths and 4 hundredths
Veronika [31]
4 tenths and 2 hundreths.
4 0
3 years ago
Read 2 more answers
HURRY I NEED HELP I GOT 21 QUESTIONS!
kati45 [8]

Answer:

Red (-2,5)

take the x = -4 and substitute into f(-4+2) = f(-2)

Step-by-step explanation:

I hope it helps

8 0
3 years ago
What is the answer to this question?! answer quick please!
Verizon [17]

Answer:

Step-by-step explanation:

1. 8 seconds

2. 15 quarts

8 0
3 years ago
Write the equation for the line that goes through the point (5, 12) with a slope m = 10​
Iteru [2.4K]

Answer:

<u>Point-slope form</u>:  y - 12 = 10 (x - 5)

<u>Slope-Intercept form</u>:  y= 10x - 38

Step-by-step explanation:

 im not fully sure which equation ur looking for but i think thats right lol. hopefully this helps ! :)

3 0
2 years ago
Other questions:
  • How to verify frac(sec theta/ csc theta- cot theta -frac(sectheta/csc theta +cot theta = 2csc theta
    7·1 answer
  • Pls help with this!!!!
    5·1 answer
  • Order these fractions from least to greatest 3/8, 2/3, 4/5
    6·1 answer
  • Given: m∠V=103°, m∠VRT=71°, RS ∥ VU Find: m∠TRS, m∠U
    15·1 answer
  • Solve by substitution
    11·1 answer
  • The answer to 7/12 divided by 2
    13·1 answer
  • Draw a A PQR if PQ = 6.5cm, m&lt; PQR=75 °and m &lt;PRQ=45° using ruler and compasses<br>only.
    15·1 answer
  • What is the algebra mat below models the equation x- 2 =4​
    6·2 answers
  • 8. Use mental math to multiply. a) 235 times 0.1, b) 235 times 0.01, c) 876 times 0.01, d) 876 times 0.001,
    5·1 answer
  • Someone do this please
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!