Question

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

1. nguyetanh
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:
#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