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
professor190 [17]
1 year ago
15

Identify the interval on which the quadratic function is positive.

Mathematics
1 answer:
Alenkasestr [34]1 year ago
3 0

Answer:

\textsf{1. \quad Solution:  $1 < x < 4$,\quad  Interval notation:  $(1, 4)$}

\textsf{2. \quad Solution:  $-2 < x < 4$,\quad  Interval notation:  $(-2, 4)$}

Step-by-step explanation:

<h3><u>Question 1</u></h3>

The intervals on which a <u>quadratic function</u> is positive are those intervals where the function is above the x-axis, i.e. where y > 0.

The zeros of the <u>quadratic function</u> are the points at which the parabola crosses the x-axis.  

As the given <u>quadratic function</u> has a negative leading coefficient, the parabola opens downwards.   Therefore, the interval on which y > 0 is between the zeros.

To find the zeros of the given <u>quadratic function</u>, substitute y = 0 and factor:

\begin{aligned}y&= 0\\\implies -7x^2+35x-28& = 0\\-7(x^2-5x+4)& = 0\\x^2-5x+4& = 0\\x^2-x-4x+4& = 0\\x(x-1)-4(x-1)&= 0\\(x-1)(x-4)& = 0\end{aligned}

Apply the <u>zero-product property</u>:

\implies x-1=0 \implies x=1

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

Therefore, the interval on which the function is positive is:

  • Solution:  1 < x < 4
  • Interval notation:  (1, 4)

<h3><u>Question 2</u></h3>

The intervals on which a <u>quadratic function</u> is negative are those intervals where the function is below the x-axis, i.e. where y < 0.

The zeros of the <u>quadratic function</u> are the points at which the parabola crosses the x-axis.  

As the given <u>quadratic function</u> has a positive leading coefficient, the parabola opens upwards.   Therefore, the interval on which y < 0 is between the zeros.

To find the zeros of the given <u>quadratic function</u>, substitute y = 0 and factor:

\begin{aligned}y&= 0\\\implies 2x^2-4x-16& = 0\\2(x^2-2x-8)& = 0\\x^2-2x-8& = 0\\x^2-4x+2-8& = 0\\x(x-4)+2(x-4)&= 0\\(x+2)(x-4)& = 0\end{aligned}

Apply the <u>zero-product property</u>:

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

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

Therefore, the interval on which the function is negative is:

  • Solution:  -2 < x < 4
  • Interval notation:  (-2, 4)
You might be interested in
Which of the following is equivalent to<br> 4x+28
weeeeeb [17]

I would answer the question but there are no answer choices, so if you could add that maybe I could help! :)

8 0
2 years ago
Read 2 more answers
IF U ANSWER THIS U ARE SWAG
Andrews [41]
Equilateral: "equal"-lateral (lateral means side) so they have all equal sides. Isosceles: means "equal legs", and we have two legs, right? Also iSOSceles has two equal "Sides" joined by an "Odd" side. Scalene: means "uneven" or "odd", so no equal sides.
8 0
2 years ago
in how many ways of the permutations of 10 different things taken 4 at a time will one particular thing always occur​
olganol [36]

Answer:

do as direct

which one of the following is square of 4

2

8

16

64

4 0
3 years ago
Susie wants to buy a snowboard that cost $530. She has already saved $98 for it. She makes $72 a week babysitting. Which inequal
Alex777 [14]
Its B , 6 because if you subtract 98 from 530 you get 432 and if you divide that by 72 you get 6 :)

6 0
3 years ago
A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year. Write
horrorfan [7]
7.5% is 3/40. The equation is y=15250(1-3/40)ˣ=15250(37/40)ˣ.
When x=8 this becomes $8173.42.
3 0
3 years ago
Other questions:
  • How any ounces is in a quart ?
    6·2 answers
  • Which statement is true about the relationship y = |x|?
    5·1 answer
  • A box contains 14 candy bars of equal weight the weight of the empty box is 10 ounces and the total weight of the box and the ca
    14·1 answer
  • Multiply (−4) × (−2) × (−5).<br><br> A. −40<br> B. −8<br> C. 8<br> D. 40
    7·2 answers
  • Can someone help me ASAP
    9·1 answer
  • roy use sone fourth cup of batter for each muffin. make a list to show the amounts of batter he will use depending on the number
    10·1 answer
  • Simplify the expression: 4(x+1)−12(x−2)
    11·2 answers
  • Sara has 13 books in her library. She bought several books at a yard sale over the weekend. She now has 63 books in her library.
    7·1 answer
  • Go step by step to reduce the radical.<br> √ 128<br><br> √16 • √8<br><br> 8 √2<br><br> 8 √4 • √2
    9·1 answer
  • Select the line plot that represents the given ages of students in a youth choir.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!