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
Harrizon [31]
3 years ago
12

Without drawing the graph of the equation answer the question. How many points does the given equation have in common with the x

-axis and where is the vertex in relation to the x-axis? y=x^2-12x+12
Mathematics
1 answer:
Alexandra [31]3 years ago
5 0

Answer:

There are two points common with the x-axis

The vertex is under the x-axis by 24 units at x = 6

Step-by-step explanation:

* For the quadratic equation y = ax² + bx + c

- The roots of the equation are the intersection point between

  the equation and the x-axis ⇒ y = 0

- To find these roots we factorize the equation into two factors

  and equate each factor with zero

- The graph of the quadratic equation is called parabola,

 the parabola has vertex point. If the vertex point is (h , k)

∴ h = -b/2a, where b is the coefficient of x and is the coefficient of x²

∴ k = y where x = h

* Lets solve the problem

∵ y = x² - 12x + 12

- The formula to find the values of x when y = 0 is

 x=\frac{-b+\sqrt{b^{2}-4ac}}{2a},x=\frac{-b-\sqrt{b^{2}-4ac}}{2a}

∵ a = 1 , b = -12 , c = 12

∴ x=\frac{-(-12)+\sqrt{(-12)^{2}-4(1)(12)}}{2(1)}=\frac{12+\sqrt{144-48}}{2}

∴ x=\frac{12+\sqrt{96}}{2}=\frac{12+4\sqrt{6}}{2}=6+2\sqrt{6}

∴ The two roots are 6 + 2√6 and 6 - 2√6

* There are two points common with the x-axis

* Lets calculate the vertex

∵ h = -b/2a

∵ b = -12 and a = 1

∴ h =-(-12)/2(1) = 12/2 = 6

∴ k = (6²) - 12(6) + 12 = 36 - 72 + 12 = -24

∴ The vertex is (6 , -24)

* That means the vertex is under the x-axis by 24 units at x = 6

You might be interested in
16) The manager of a bulk foods establishment sells a trail mix for $8 per
zaharov [31]

Answer:

The amount of peanuts to use is 5 pounds and that of cashews is 30 pounds.

Step-by-step explanation:

Let the amount of peanut to use to be x

Let the amount of cashews to use to be 35-x

Form equations to compare amounts for individual foods and the mixture

8x+15(35-x)=35(14)\\\\8x+525-15x=490\\\\7x=35\\\\x=5\\\\

So the pounds to be used for peanuts is 5 pounds

The pounds to be used for cashews will be 35-x= 35-5=30 pounds

Learn More

Mixtures : brainly.com/question/11497620

Keywords : Mixture

#LearnwithBrainly

5 0
3 years ago
Write a polynomial that is a trinomial, has the coefficients 3 and 4, the variable x,
vladimir1956 [14]

Answer:

3x+4x+7

Step-by-step explanation:

First, a Trinomial consists of three terms.

so we have <u>blank</u>+<u>blank</u>+<u>blank</u>

Next we need to add the coefficients.

<u>3</u>+<u>4</u>+<u>blank</u>

Add the variables.

3x+4x+<u>blank</u>

And lastly, add the constant.

3x+4x+7

Good luck!

8 0
3 years ago
Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n &gt; 1? 9.6, 4.8, 2.4, 1.2, 0.6, ..
White raven [17]
Hello,

The formula is f(n)= \dfrac{f(n-1)}{2}&#10;&#10;
4 0
3 years ago
Help algebra 2 please
kati45 [8]

Answer:

Step-by-step explanation:

(f*g)(x) = (-5x² + 2x + 7) (x +1)

          = x* (-5x² + 2x + 7) + 1*(-5x² + 2x + 7)

          = x*(-5x²) + x*2x + x*7 - 5x² + 2x + 7

        = -5x³ + 2x² + 7x - 5x² + 2x + 7

        = - 5x³ + <u>2x² -5x²</u>   <u>+ 7x + 2x </u>+7   {Combine like terms}

       =  -5x³ - 3x² + 9x + 7

4) (f*g)(x) = (x² + 2x + 4)(x - 2)

                = x*(x² + 2x + 4) - 2*(x² + 2x + 4)

                = x*x² + x*2x + x*4 - 2*x² - 2*2x -2* 4

                = x³ + 2x² + 4x  -2x² -4x - 8

                = x³ - 8

2) Speed=\dfrac{distance}{time}\\\\\\= \dfrac{d(h)}{t(h)}\\\\= \dfrac{2\sqrt{h}}{3\sqrt{4h}}=\dfrac{2*\sqrt{h}}{3*2\sqrt{h}}\\\\\\=\dfrac{1}{3}

1)d(h) = \sqrt{16h^{4}}=\sqrt{2*2*2*2*h*h*h*h}=2*2*h*h=4h^{2}\\\\\\t(h) = 3h^{4}-3h^{3}-5h^{2}= h^{2}(3h^{2}-3h - 5))\\\\Speed=\dfrac{4h^{2}}{h^{2}(3h^{2}-3h-5)}\\\\=\dfrac{4}{3h^{2}-3h-5}

7 0
3 years ago
You are given f(x)=-5x2+10x-5
Bond [772]

Answer:

B

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to
    13·1 answer
  • Please help i dont want to fail..
    8·2 answers
  • I NEED HELP ASAP PLS ANSWERR
    15·1 answer
  • State the slope and y-intercept of the equation, y = -2x – 8
    15·2 answers
  • Hellppp 8(–10r+–1)+–r+2
    13·1 answer
  • Identify the graph containing the point (1,−5) .
    7·1 answer
  • I need help on number 19 and 20
    10·2 answers
  • What is the justification (reason) for the statement below?
    6·1 answer
  • An equilateral triangle has a perimeter of 15x3 33x5 feet. what is the length of each side? x3 feet 5 11x2 feet 5x2 11 feet 5x3
    14·1 answer
  • Factor the polynomial expression 3x² + 2.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!