What is the value of h when the function is converted to vertex form? note: vertex form is p(x)=a(x−h)2+k . p(x)=x2−14x+29 enter your answer in the box.

p(x) = (x - 7)^2 -20

Step-by-step explanation:

Convert p(x)=x^2−14x+29 to vertex form, to resemble y = (x - h)^2 + k, where (h, k) is the vertex:

1. Rewrite p(x)=x^2−14x+29 as p(x)=x^2 − 14x +                                   +29

2. Identify the coefficient of the x term:  It is -14.

3.  Take HALF of this coefficient:  it is -7

4.  Square this result, obtaining 49

5.  Add this to x^2 − 14x and then subtract it, keeping the +29:

    x^2 - 14x + 49 - 49 + 29

6.  Rewrite the first three terms as the square of a binomial:

     p(x) = (x - 7)^2           -49 + 29, or

      p(x) = (x - 7)^2 -20      This is the desired result (answer).

7.   If you want to  identify the vertex, compare this

   p(x) = (x - 7)^2 -20 to the standard form

      f(x) = (x - h)^2 + k               Then h = 7 and k = -20.

8.    The vertex of the parabolic graph of this function is (7, -20).

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step-by-step explanation: