+0  
 
+1
41
4
avatar+274 

hello everyone,

 

The equation of a parabola is given: 

\(f(x)=-x^2-x+6\)

 

If \(h(x)\) is a reflection of \(f(x)\) about the x-axis, determine it's equation if the graph is shifted 3 units to the right. leave your answer in the form: \(a(x+p)+q\)

 

Okay, the following I understand:

 

\(- x^2-x+6\),  becomes  \(x^2+x-6\) (Reflection)

 

now add the shift: \({(x-3)}^2+(x-3)-6\)

 

This equates to: \(x^2-5x\)

 

NOW THIS PART:

 

\(h(x)=(x-{5 \over2})^2-{25 \over4}\)

 

Please explain this last part...Thank you all kindly..

juriemagic  Nov 2, 2018
 #1
avatar+2729 
+1

\(\text{just complete the square}\\ x^2 - 5x = \\ \\ x^2 - 5x + \dfrac{25}{4} - \dfrac{25}{4} = \\ \\ \left(x-\dfrac 5 2\right)^2 - \dfrac{25}{4}\)

Rom  Nov 2, 2018
 #2
avatar+274 
+2

Hi Rom,

 

but why \(25 \over 4\)?

 

or \(5 \over2\) in the first place?..I just don't get this..

juriemagic  Nov 2, 2018
edited by juriemagic  Nov 2, 2018
 #3
avatar+93866 
+2

 

 

\(h(x)=x^2-5x\\ \)

 

I'll use a different concrete example to start with

\((x-6)^2=x^2-2*6x+36\\ (x-\frac{12}{2})^2=x^2-12x+(\frac{12}{2})^2\\ x^2-12x+(\frac{12}{2})^2=(x-\frac{12}{2})^2\\~\\ \text{So for your question}\\ x^2-5x+(\frac{5}{2})^2=(x-\frac{5}{2})^2\\ \text{which means}\\ x^2-5x+(\frac{5}{2})^2-(\frac{5}{2})^2=(x-\frac{5}{2})^2-(\frac{5}{2})^2\\ x^2-5x=(x-\frac{5}{2})^2-(\frac{5}{2})^2\\ x^2-5x=(x-\frac{5}{2})^2-(\frac{25}{4})\\ \)

 

So here, both Rom and I have 'completed the square'  

 

Is that any clearer?

Melody  Nov 2, 2018
 #4
avatar+274 
+2

wow..Melody....yes, it's clearer thank you...I have to admit, I'm going to have to sit with this for a little more, but I'm sure the light will come on!!!... smiley..Thank you very much...and to you also Rom..Have a great weekend!!

juriemagic  Nov 2, 2018

38 Online Users

avatar
avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.