Question

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.

Answer 1

Answer:

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).

Answer 2

The value of h when the provided function is converted to standard vertex form is 7.

What is vertex form of parabola?

Vertex form of parabola is the equation form of quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

$y=a(h-x)^2+k$

Here, (h, k) is the vertex point.

The given quadratic equation is,

$p(x)=x^2-14x+29$

Here, square of the half of the middle term (-14) is 49. Thus add and subtract this number from the above equation a,s

$p(x)=x^2-14x+29+49-49\\p(x)=x^2-14x+49+29-49\\p(x)=(x^2-14x+49)+(29-49)$

Using the property of whole square, the above equation can be written as,

$p(x)=(x-7)^2+(-20)\\p(x)=(1)(x-7)^2+(-20)$

This is the vertex form of the given equation. Compare it with the standard vertex form we get,

$a=1\\h=7\\k=-20$

Hence, the value of h when the provided function is converted to standard vertex form is 7.

Learn more about the vertex form of the parabola here;

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