complete the square and find the vertex for of the quadratic function

Question

f (x)=x²-10+96

Answer 1

f(x)=x²-10x+96        

 

Jodi, I bet you left out the "x"  following the number 10.

First, you complete the square by taking half the coefficient of "x" and                       squaring it.

 

-10          (-5)²=25

  2

 

Next, you add and subtract 25.

f(x)=(x²-10x+25)+96-25

f(x)=(x-5)(x+5)+71

F(x)=(x-5)²+71

 

Vertex: (5,71)

Answer 2

Hello, Jodi from :) Texas

 

Ok.  There will be no real solutions for this problem.

 f(x)= x^2-10x+ 96    

 0=.       x^2-10x+96                   Subtract 96 from both sides.

-96                      -96

 -96    = x^2-10x                     Take the 10/2=5 and square it. That

 +25.                  +25               will be 25. Add 25 to both sides.

    -71= x^2-10x+ 25.              Factoring

    -71= (x-5)^2                       Taking the sq. rt. of both sides.

 

Let me stop for a second.  I don't know whether you have learned about complex numbers or not. You cannot take the square root of a negativE number. So, I am going to use complex numbers.  The sq. rt. of -71 is equal to 71i.  Let's continue with the problem.  When you take the square root of some number, you have two possible answer.  For example, the sq. rt. of  16 is -4 and 4.  Why? Because (4)(4)=16 so is (-4)(-4).  

 

We we this is what we have

-71= (x-5)^2                       Take the sq. root of both sides

71i = x-5          or       -71i = x-5

71i+5= x          or        -71i+ 5= x

 

Oh, with all the excitement, I forgot the vertext.  You can glean the vervex of the parabola by looking at its standard form.  The standard form is:

ax^2+bx+c= 0               Note that this problems is in the standard form. So, I am going to substitute.

 1x^2-10x+96=0            a=1, b= -10, c=96

 

The formula for the vertex is

 

[-(b)]/[2(a)]                   Substituting for a and b

[-(-10)]/[2(1)]

    10/2

       5                             That is the value of the x-coordinate of the vertex. 

 

To find the y-coordinate of the vertex, substitute 5 for x into x^2-10x+96

                                                                                      (5)^2-10(5)+86

                                                                                          25-50+96

                                                                                               71

 

So, the coordinate for the vertex is (5, 71)

 

So, finally, there you have it.  I hope this helps.  And, thanks for posting. 

D. Y. Taylor

 Don't forget to rate my answer :)