We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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**+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**+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

#3**+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**+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!!!... ..Thank you very much...and to you also Rom..Have a great weekend!!

juriemagic
Nov 2, 2018