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
S_A_V [24]
2 years ago
13

Find the x-intercepts of the parabola with

Mathematics
2 answers:
12345 [234]2 years ago
8 0

Answer:

x-intercepts are (0, 0) and (-6, 0)

Step-by-step explanation:

equation of a parabola in vertex form:  y = a(x - h)² + k

where (h, k) is the vertex

Substituting the given vertex (-3, -18) into the equation:

y = a(x + 3)² - 18

If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:

0 = a(0 + 3)² - 18

⇒ 0 = a(3)² - 18

⇒ 0 = 9a - 18

⇒ 9a = 18

⇒ a = 2

Therefore, y = 2(x + 3)² - 18

To find the x-intercepts, set the equation to 0 and solve for x:

                                 2(x + 3)² - 18 = 0

Add 18 to both sides:     2(x + 3)² = 18

Divide both sides by 2:    (x + 3)² = 9

Square root both sides:      x + 3 = ±3

Subtract 3 from both sides:  x = ±3 - 3

so x = 3 - 3 = 0  

and  x = -3 - 3 = -6

So x-intercepts are (0, 0) and (-6, 0)

skelet666 [1.2K]2 years ago
3 0

<u>Answer</u>:

The x-intercepts are ( 0 , 0 ) , ( -6 , 0 )

<u>Explanation</u>:

vertex (-3,-18) and y-intercept (0,0)

equation used f(x) = a(x - h)² + k  where (h,k) is vertex.

0 = a(0--3)² + -18

0 = 9a - 18

18 = 9a

a = 2

f(x) = a(x - h)² + k  ......this is vertex to find equation of parabola.

f(x) = 2(x - -3)² + -18

f(x) = 2(x + 3)² - 18 ....this is our formula of parabola

f(x) = 2(x² +6x + 9) - 18

f(x) = 2x² +12x +18 - 18

f(x) = 2x²+12x  .....if simplified.

To find x intercepts, y must be 0,

2x²+12x = 0

2x(x+6) = 0

x = 0 , -6

so the coordinates are: ( 0 , 0 ) , ( -6 , 0 )

You might be interested in
What is the factorization??
aivan3 [116]

We first find the zeros of the function , the zeros of the function are those at which points the graph of the function crosses or touches the x axis

here we can see in the graph that graph crosses the x axis at two points , 1 and 7

So the zeros of the function are

x=1 and x=7

It means the factor are

(x-1) and (x-7)

So the factorization is given by

(x-1)(x-7)

7 0
3 years ago
Find area of a rectangle that measures 18yd by 14yd
adell [148]

Answer:

32.

Step-by-step explanation:

5 0
3 years ago
a box 750 grams. there are 25 such boxes. what is the total weight of the boxes in kilograms? give your answer to the nearest te
madam [21]
750 x 25 = 18750 grams
there are 1,000 grams in a kilogram, so divide 18750 by 1,000 to get 18.750 kilograms. Rounded to the nearest tenth is 18.8 kilograms
6 0
3 years ago
PLZZ HURRY<br><br>q1) <br>Simplify. 6(5p^3 − 6p)
AlexFokin [52]

Answer:

30p^3−36p

Step-by-step explanation:

6(5p^3−6p)

=(6)(5p^3+−6p)

=(6)(5p^3)+(6)(−6p)

=30p3−36p

6 0
3 years ago
Read 2 more answers
What’s the volume of this
pav-90 [236]

Given:

The height of the cylinder = 12 in

The diameter of the base of the cylinder = 8 in.

To find:

The volume of the cylinder.

Solution:

The diameter of the base of the cylinder is 8 in. The radius is half of its diameter. So,

r=\dfrac{8}{2}

r=4

So, the radius of the base of the cylinder is 4 in.

The height of the cylinder, h = 12 in.

Base area of the cylinder is:

B=\pi r^2

Where, B is the base area and r is the radius.

B=\pi (4)^2

B=16\pi

So, the base area is 16\pi square inches.

The volume of the cylinder is:

V=\pi r^2h

V=Bh

Where, r is radius, h is height, B is base area.

Putting B=16\pi and h=12, we get

V=(16\pi )12

V=192\pi

So, the volume is 192\pi cubic inches.

Therefore, r=4\text{ in}, h=12\text{ in},B=16\pi \text{ in}^2,V=192\pi \text{ in}^3.

7 0
3 years ago
Other questions:
  • 72,500/2=?<br> 72,500/4=?<br> 72,500/6=?<br> Add all.<br> =?
    15·2 answers
  • 5. Two similar figures have volumes 27 in.? and 125 in.?. The surface area of the smaller figure is 63 in.. (1 point)
    10·1 answer
  • Solve each proportion. What is the soulution to M/10=10/3
    14·1 answer
  • Need help thanks???!!
    13·1 answer
  • Five names for number 64
    10·1 answer
  • Which graph represents the inequality x≥2?
    14·2 answers
  • What is y=-x+3<br> y=-7x-3 <br> A.) (-4,-4)<br> B.) (-4,4)<br> C.) (4,-2)<br> D.) (-1, 4)
    15·1 answer
  • The input of days results in the output of total collected books. On day 1, 8 books were collected. Both inputs for days 2 and 3
    9·1 answer
  • Translate the following:<br> One half of a number (use x) is equal to 8 less than the same number.
    15·2 answers
  • 4 minutes, 14 seconds = ____ seconds
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!