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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answered: 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

answered: 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

answered: Guest

-18 degrees is the answer : )

answered: Guest

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