Question

Write the quadratic function
`f(x)=(1)/(7) (x^(2) +14x+35)` in standard form and use it to find the axis of symmetry and the vertex.

Answer 1

f(x) = 1/7 * (x + 7)^2 - 2

axis of symmetry: x = -7

vertex: (-7 | -2)

Explanation:

f(x) = 1/7 * (x^2 + 14x + 35)

f(x) = 1/7 * (x^2 + 14x) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7

f(x) = 1/7 * (x + 7)^2 + 5 - 7

f(x) = 1/7 * (x + 7)^2 - 2