Question

Write the quadratic function in the form f(x) = a * (x - h) ^ 2 + k Then, give the vertex of its graph. f(x) = x ^ 2 - 8x + 19

Answer 1

Writing in the form specified: f(x) = (x - 4)² + 3

Vertex: (4, 3)

Step-by-step explanation:

The given equation is

f(x) = x² - 8x + 19

To write it in vertex form, we need to add and subtract (b/2)², where b is the number beside x. In this case, b = -8, so

(b/2)² = (-8/2)² = (-4)² = 16

Then, if we add and subtract 16, we get

f(x) = x² - 8x + 19 + 16 - 16

f(x) = (x² - 8x + 16) + (19 - 16)

f(x) = (x - 4)² + 3

Therefore, in the form f(x) = a(x - h)² + k, a = 1, h = 4 and k = 3.

Therefore, the vertex is

(h, k) = (4, 3)

So, the answers are

Writing in the form specified: f(x) = (x - 4)² + 3

Vertex: (4, 3)