What are the vertex focus and directrix of the parabola with the given equation y = 1/28(x - 4)² - 5

Solution:

We know that the equation of a parabola is

(x - h)² = 4p(y - k)

Where (h, k) is the vertex

(h, k + p) is the focus

y = k - p is the directrix

The given equation is

y = 1/28(x - 4)² - 5

By further calculation

(x - 4)² = 28 (y + 5)

From this we know that

(h, k) = (4, -5)

p = 7

So the focus (h, k + p) = (4, 2)

Directrix y = k - p = - 5 - 7 = -12

Therefore, the vertex is (4, -5), focus is (4, 2) and directrix is -12.

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What are the vertex focus and directrix of the parabola with the given equation y = 1/28(x - 4)² - 5

Summary:

The vertex, focus and directrix of the parabola with the given equation y = 1/28(x - 4)² - 5 is (4, -5), (4, 2) and -12.