Write the domain AND range of the following graph.

Given:

The graphs of two parabolas.

To find:

The equation of the quadratic function with given graphs.

Solution:

(a)

The factor form of a parabola is

[tex]y=a(x-b)(x-c)[/tex]

Where, a is a constant, b and c are x-intercepts.

From the graph (a) it is clear that the graph intersect the x-axis at -1 and 3. So, b=-1 and c=3.

[tex]y=a(x-(-1))(x-3)[/tex]

[tex]y=a(x+1)(x-3)[/tex]            ...(i)

Put x=0 and y=3 because the y-intercept is (0,3).

[tex]3=a(0+1)(0-3)[/tex]

[tex]3=-3a[/tex]

[tex]\dfrac{3}{-3}=a[/tex]

[tex]-1=a[/tex]

Putting a=-1 in (i), we get

[tex]y=-1(x+1)(x-3)[/tex]

[tex]y=-(x+1)(x-3)[/tex]

Therefore, the equation of the parabola is [tex]y=-(x+1)(x-3)[/tex].

(b)

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]

Where, a is a constant and (h,k) is vertex.

From the the graph (b), it is clear that the vertex of the of the parabola is at point (2,0) and y-axis is (0,8). So, h=2, k=0.

[tex]y=a(x-2)^2+0[/tex]

[tex]y=a(x-2)^2[/tex]            ...(ii)

Put x=0 and y=8 because the y-intercept is (0,8).

[tex]8=a(0-2)^2[/tex]

[tex]8=4a[/tex]

[tex]\dfrac{8}{4}=a[/tex]

[tex]2=a[/tex]

Putting a=2 in (ii), we get

[tex]y=2(x-2)^2[/tex]

Therefore, the equation of the parabola is [tex]y=2(x-2)^2[/tex].

Answer:

-28

Step-by-step explanation:

Answer:

s=[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Answer:

1.) It is not a valid sample because it is only a short study

Step-by-step explanation:

Answer:

1.) It is not a valid sample because it is only a short study

Step-by-step explanation:

Hope this helped!! :)

Stay safe and have a wonderful afternoon!!!!!

Answer:

[tex]x > \frac{1}{4} [/tex]

Step-by-step explanation:

[tex]12x - 5 > - 2[/tex]

Lets add +5 in both the sides.

[tex] = > 12x - 5 + 5 > - 2 + 5[/tex]

[tex] = > 12x > 3[/tex]

Now lets divide 12 on both the sides.

[tex] = > \frac{12x}{12} > \frac{3}{12} [/tex]

[tex] = > x > \frac{1}{4} [/tex]

Answer:

29/90

Step-by-step explanation:

0.32     x10

3.22     -0.32

2.9       /9

2.9/9    x10/10

29/90

Answer:

29/90

Step-by-step explanation:

here if

f=0.32222....... — 1

10f=3.2222...... —2

now eq2-eq1

we get

9f=2.9

f=2.9/9

f=29/90

Answer:

6/5

Step-by-step explanation:

1 would equal 5/5 so add another 1 to get 6/5

Answer:

1/16

Step-by-step explanation:

(1/4)^2=16

Answer:

Circumference=diameter x pie

=(17.5×2)×pi

=35pi

Answer:

35π cm

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 17.5 = 35π cm

Answer:

2nd choice

Step-by-step explanation:

1. dilation factor: 1/2

2. rotation: about origin anti-clockwise 180°

Δ ABC - Δ A'B'C', because AA'B'C' is obtained by dilating AABC by a scale factor of 1/2 and then rotating it about the origin by 180 degrees.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We have to find the statement which is correct for triangle ABC and triangle A'B'C'.

Let us find the coordinates of triangle ABC

A=(2, 2), B=(2, 10) and C=(8, 12)

After transformation the triangle A'B'C'.

Coordinates A' = (-1, -1), B(-1, 5) and C'(-4, 6)

The scale factor is 1/2.

A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size.

Δ ABC - Δ A'B'C', because AA'B'C' is obtained by dilating AABC by a scale factor of and then rotating it about the origin by 180 degrees.

Hence, Δ ABC - Δ A'B'C', because AA'B'C' is obtained by dilating AABC by a scale factor of 1/2 and then rotating it about the origin by 180 degrees.

To learn more on Graph click:

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Answer:

14.25 decimal para saken

{2l+2w=62}

1-2w=1

I don't know the answer its not in my syllabus nor I was thought this one

Answer:

C) 4

Step-by-step explanation:

I hope this helps :)

Answer:

24cm

Step-by-step explanation:

A^2 + B^2 = C^2 soo 10^ + B^ = 26^2 so 100 + B^2 = 676 subtract 100 from 676. Then take the square root of 576 and you’ll get 24. So B = 24cm

Answer:

Step-by-step explanation:

14(13)12=2184

Answer:

y=25x+4

Step-by-step explanation:

Answer:

c = 16

Explanation:

Do it on a calculator it'll be correct