Question

Given ​ f(x)=x2+14x+40. Enter the quadratic function in vertex form in the box.

Answer 1

For this case we have an equation of the form:
 $y = ax ^ 2 + bx + c$
 This equation in vertex form is:
 $f (x) = a (x - h) ^ 2 + k$
 where (h, k) is the vertex of the parabola.
 We have the following function:
 $f (x) = x ^ 2 + 14x + 40$
 We look for the vertice.
 For this, we derive the equation:
 $f '(x) = 2x + 14$
 We equal zero and clear the value of x:
 $2x + 14 = 0 2x = -14 x = -14/2 x = -7$
 Substitute the value of x = -7 in the function:
 $f (-7) = (- 7) ^ 2 + 14 * (- 7) +40 f (-7) = -9$
 Then, the vertice is:
 $(h, k) = (-7, -9)$
 Substituting values we have:
 $f (x) = (x + 7) ^ 2 - 9$
 Answer:
 The quadratic function in vertex form is:
 $f (x) = (x + 7) ^ 2 - 9$