Answers

1. The value of k is (A) 20/3.

   What is a parabola?

   • A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics.
   • It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.
   • A point and a line are two ways to describe a parabola.

   To find the value of k:

   • y – b = c (x – a)²

   Where (a, b) is the vertex and c is the constant.

   • (a, b) = (-4, k)
   • y – k = c (x – (- 4))²
   • y – k = c (x + 4)²

   So,

   • x = 0, y = 12
   • 12 – k = 16c
   • k = 12 – 16c  …… (1)

   Then,

   • (-3, 7) = (x, y)
   • 7 – k = c (1)²
   • k = 7 – c  …… (2)

   Now,

   • 12 – 16c = 7 – c
   • 12 – 7 = 16c – c
   • 5 = 15c
   • c = 5/15 = 1/3

   So, the value of k:

   • k = 12 – 16 (1/3) = 12 – 16/3 = 36-16/3 = 20/3

   Therefore, the value of k is (A) 20/3.

   Know more about a parabola here:

   https://brainly.com/question/4061870

   #SPJ4

   The complete question is given below:

   The coordinates of the vertex of a parabola in the XY plane are (-4,k). If the y-intercept of the parabola is 12 and the parabola passes through the point (-3,7), then what is the value of k?

   (A) 20/3

   (B) 16/5

   (C) 14/3

   (D) 12/5

   Reply