Mathematics, 20.09.2020 18:01 Anliz0179

Write the equation of each parabola in vertex form a. Vertex: (-3, 7); Point:(-2, -5) b. Vertex: (1, 3); Point: (2, 5) c. Vertex: (-4, 6); Point: (-2, -2) d. Vertex: (7, 4); Point: (5, 16)

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Answer from: seasmarie75

a) The equation of the parabola is $y+3 = -12\cdot (x-7)^{2}$ .

b) The equation of the parabola is $y-3 = 2\cdot (x-1)^{2}$ .

c) The equation of the parabola is $y-6 = -2\cdot (x+4)^{2}$ .

d) The equation of the parabola is $y-4 = 3\cdot (x-7)^{2}$ .

The equation of the parabola in vertex form is described below:

$y-k = C\cdot (x-h)^{2}$ (1)

Where:

- Independent variable.

- Dependent variable. h,k

- Vertex coordinates.

- Vertex constant.

The vertex constant is found by (1):

$C = \frac{y-k}{(x-h)^{2}}$

Now we proceed to determine each equation of the parabola:

a) (h, k) = (-3, 7), (x, y) = (-2, -5)

$C = \frac{-5-7}{(-2+3)^{2}}$

C = -12

The equation of the parabola is $y+3 = -12\cdot (x-7)^{2}$ .

b) (h, k) = (1, 3), (x, y) = (2, 5)

$C = \frac{5-3}{(2-1)^{2}}$

C = 2

The equation of the parabola is $y-3 = 2\cdot (x-1)^{2}$ .

c) (h, k) = (-4, 6), (x, y) = (-2, -2)

$C = \frac{(-2-6)}{(-4+2)^{2}}$

C = -2

The equation of the parabola is $y-6 = -2\cdot (x+4)^{2}$ .

d) (h, k) = (7, 4), (x, y) = (5, 16)

$C = \frac{(16-4)}{(5-7)^{2}}$

C = 3

The equation of the parabola is $y-4 = 3\cdot (x-7)^{2}$ .

We kindly invite to check this question on parabolas: link

Answer from: bcaughman6885

a) y = 2(x + 3)² - 7

b) y = -2(x + 4)² + 6

c) y = 3(x - 7)² + 4

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k where

"a" is the vertical stretch(h, k) is the vertex(x, y) is any point on the curve

Input (h, k) and (x, y) to solve for "a"

a) (h, k) = (-3, 7) and (x, y) = (-2, -5)

-5 = a(-2 + 3)² - 7

2 = a(1)²

2 = a

y = 2(x + 3)² - 7

b) (h, k) = (1, 3) and (x, y) = (2, 5)

5 = a(2 - 1)² + 3

2 = a(1)²

2 = a

y = 2(x - 1)² + 3

c) (h, k) = (-4, 6) and (x, y) = (-2, -2)

-2 = a(-2 + 4)² + 6

-8 = a(2)²

-8 = 4a

-2 = a

y = -2(x + 4)² + 6

d) (h, k) = (7, 4) and (x, y) = (5, 16)

16 = a(5 - 7)² + 4

12 = a(-2)²

12 = 4a

3 = a

y = 3(x - 7)² + 4

Answer from: Quest

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3

Can someone plz answer this for me? whoever answers it first, i will give !

Answer from: Quest

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation:

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Write the equation of each parabola in vertex form a. Vertex: (-3, 7); Point:(-2, -5) b. Vertex: (1,...

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