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
blagie [28]
1 year ago
10

Dentify on which quadratic function is positive.

Mathematics
2 answers:
Olin [163]1 year ago
4 0

Answer:

\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}

\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}

Step-by-step explanation:

A function is positive when it is <u>above the x-axis</u>, and negative when it is <u>below the x-axis</u>.

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

<u>Given quadratic equation</u>:

y = 2x^2 - 17x + 30

Factor the equation:

\implies y = 2x^2 - 17x + 30

\implies y = 2x^2 - 5x-12x + 30

\implies y=x(2x-5)-6(2x-5)

\implies y=(x-6)(2x-5)

The x-intercepts of the parabola are when y = 0.

To find the <u>x-intercepts</u>, set each factor equal to zero and solve for x:

\implies x-6=0 \implies x=6

\implies 2x-5=0 \implies x=\dfrac{5}{2}

Therefore, the x-intercepts are x = ⁵/₂ and x = 6.

The leading coefficient of the given function is positive, so the <u>parabola opens upwards</u>.  

The function is positive when it is <u>above the x-axis</u>.

Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:

  • \textsf{Solution: \quad $x < \dfrac{5}{2}$ \;and \;$x > 6$}
  • \textsf{Interval notation: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}

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

<u>Given quadratic equation</u>:

y = - x^2 - 6x - 8

Factor the equation:

\implies y = - x^2 - 6x - 8

\implies y = -(x^2 +6x +8)

\implies y = -(x^2 +4x +2x+8)

\implies y = -((x(x+4)+2(x+4))

\implies y = -(x+4)(x+2)

The x-intercepts of the parabola are when y = 0.

To find the <u>x-intercepts</u>, set each factor equal to zero and solve for x:

\implies x+4=0 \implies x=-4

\implies x+2=0 \implies x=-2

Therefore, the x-intercepts are x = -4 and x = -2.

The leading coefficient of the given function is negative, so the <u>parabola opens downwards</u>.  

The function is negative when it is <u>below the x-axis</u>.

Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:

  • \textsf{Solution: \quad $x < -4$ \;and \;$x > -2$}
  • \textsf{Interval notation: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}

Hoochie [10]1 year ago
3 0

Step-by-step explanation:

Let us identify which quadratic function is positive. Yeah, let's start.

Y = { \red{ \sf{2 {x}^{2}  - 17x + 30}}}

By using factorisation method,

{ \red{ \sf{2 {x}^{2}  - 12x - 5x + 30}}}

Take common factors

{ \red{ \sf{2x(x - 6) - 5(x - 6)}}}

{ \red{ \sf{(2x - 5)}}} \:  \:  \:  \:  \:   \:  \: ||  \:  \:  \:  \:  \: { \red{ \sf{(x - 6)}}}

{ \red{ \sf{2x - 5 = 0}}} \:  \:  ||  \:  \: { \red{ \sf{x - 6 = 0}}}

{ \red{ \sf{2x = 5}}} \:  \:  \:  \:  \:  \:  \:    \:  \:  ||  \:  \:  \:  \: { \red{ \boxed{ \green{ \sf{x = 6}}}}}

{ \red{ \sf{{ \frac{ \cancel2}{ \cancel2}x}}}} = { \red{ \sf{ \frac{5}{2}}}}

{ \red{ \boxed{ \green{ \sf{x =  \frac{5}{2}}}}}}

____________________________________

Y = { \blue{ \sf {{ - x}^{2}  - 6x - 8}}}

By using factorisation method,

{ \blue{ \sf{ -  {x}^{2}  - 2x - 4x - 8}}}

Take common factors

{ \blue{ \sf{ - x(x + 2) - 4(x + 2)}}}

{ \blue{ \sf{( - x - 4)}}} \:  \:  \:  \:  \:  ||  \:  \:  \:  \:  \: { \blue{ \sf{(x + 2)}}}

{ \blue{ \sf{- x - 4 = 0}}} \:  \:  \: \: \: || \:  \:  \:  \: \: { \blue{ \sf{x + 2 = 0}}}

{ \blue{ \boxed{ \green{ \sf{x = -4}}}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \boxed{ \green{ \sf{x = -2}}}}}

Hence, the first quadratic function is positive and second quadratic function is negative.

You might be interested in
27.) If a ≠ 0, then lim (x^2 - a^2)/(x^4 - a^4) is:<br> x-&gt;-a
oksian1 [2.3K]

Answer:

\frac{1}{2a^2}

Step-by-step explanation:

Step 1: Write limit

\lim_{x \to -a} \frac{x^2-a^2}{x^4-a^4}

Step 2: Factor

\lim_{x \to -a} \frac{(x+a)(x-a)}{(x+a)(x-a)(x^2+a^2)}

Step 3: Simplify

\lim_{x \to -a} \frac{1}{x^2+a^2}

Step 4: Substitute

\frac{1}{(-a)^2+a^2}

Step 5: Evaluate

\frac{1}{a^2+a^2}

Step 6: Simplify

\frac{1}{2a^2}

4 0
3 years ago
Could someone help me with these quickly, I'm in a hurry.
Otrada [13]
12] n is greater than or equal to -23
8 0
3 years ago
If an item
GuDViN [60]

Answer:

$1.00/6= $0.16

We can take $1.00 and divide it by 6(the amount of items bought)

This will come out to your $/each item.

5 0
3 years ago
In 2001, a company marketed 730,000 units of its product. In 2001 its yearly volume was 50% of its volume for 2004. The 2004 vol
kotykmax [81]

Answer:

4000 units

Step-by-step explanation:

In 2001 the total number of marketed units= 730,000

If this number represents 50% of what was marketed in 2004, then the total number of units marketed in 2004 was:

(100/50)× 730,000=1460000

To get the number for each of the 365 days in 2004 we divide the total for 2004 by 365

1460000/365= 4000 units

6 0
3 years ago
Read 2 more answers
You Buy 15 Notebooks For $20.25 So How Much Would Just 1 Notebook Cost?
zaharov [31]

Answer:

1.35

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • Myra swims 3/5 of a mile farther than Luke. If luke swims 2 4/10 miles. How many miles does Myra swim?
    5·1 answer
  • on a suspension bridge the roadway is hung from cables hanging between support towers. the cable of one bridge segment of the pa
    8·1 answer
  • What is the rate of the graph below?
    10·1 answer
  • Benjamin bought a 3-pound bag of flour for $6.95. What is the unit price per ounce of flour? (1 pound = 16 ounces)
    10·1 answer
  • Prove each of the following statements about integers by proving thecontrapositive of the statement.A. If 3nis even, thennis eve
    13·1 answer
  • Which inequalities are true? Select the four correct answers.
    6·1 answer
  • Mitch made a dot plot of the number of hours that students in his grade spent this week watching television. Use the data to cho
    5·2 answers
  • I need help picture below
    14·1 answer
  • The value of p in the equation 2p - 3 = p + 2 Is ​
    8·2 answers
  • Given: ABCD is a parallelogram.<br> Prove:
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!