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

Answer 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:

brainly.com/question/4061870

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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