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)

a) The equation of the parabola is .

b) The equation of the parabola is .

c) The equation of the parabola is .

d) The equation of the parabola is .

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

(1)

Where:

The vertex constant is found by (1):

Now we proceed to determine each equation of the parabola:

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

The equation of the parabola is .

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

The equation of the parabola is .

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

The equation of the parabola is .

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

The equation of the parabola is .

We kindly invite to check this question on parabolas: link

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

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

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

    5 = a(2 - 1)² + 3

     2 = a(1)²

     2 = a

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

    -2 = a(-2 + 4)² + 6

    -8 = a(2)²

    -8 = 4a

    -2 = a

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

    16 = a(5 - 7)² + 4

    12 = a(-2)²

     12 = 4a

      3 = a

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: