- #1

Callmelucky

- 144

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- Homework Statement
- Shouldn't it be ##\frac{b^{2}}{4a^{2}}## after raising (b/2a) to power of 2?

- Relevant Equations
- f(x)= ax^2 + bx + c, f(x)=a(X-Xo)^2 + Yo

Can someone please tell me where I am wrong. I am learning how to write ##a^{2} + bx + c## in this form ##f(x)= a(X-X_0)^{2} +Y_0##.

The method used in my textbook is a reduction to the perfect square. And it goes like this:

##f(x)=ax^2+bx+c##

##=a[x^2+\frac{b}{a}x]+c##

##=a\left [ x^2+\frac{b}{a}x+\left ( \frac{b}{2a} \right )^2-\left ( \frac{b}{2a} \right )^2 \right ]+c##

##=a\left ( x+\frac{b}{2a} \right )^2 -\frac{b^2}{4a}+c##

##f(x)=a\left ( x+\frac{b}{2a} \right )^2 + \frac{4ac-b^2}{4a}##

Now my question is shouldn't in the last two steps after squaring ##\frac{b}{2a}## be ##\frac{b^2}{4a^2}## and not ##\frac{b^2}{4a}## as it is written in my textbook, I have also checked on the internet but the answer is the same, although I couldn't find why.

Thank you.

The method used in my textbook is a reduction to the perfect square. And it goes like this:

##f(x)=ax^2+bx+c##

##=a[x^2+\frac{b}{a}x]+c##

##=a\left [ x^2+\frac{b}{a}x+\left ( \frac{b}{2a} \right )^2-\left ( \frac{b}{2a} \right )^2 \right ]+c##

##=a\left ( x+\frac{b}{2a} \right )^2 -\frac{b^2}{4a}+c##

##f(x)=a\left ( x+\frac{b}{2a} \right )^2 + \frac{4ac-b^2}{4a}##

Now my question is shouldn't in the last two steps after squaring ##\frac{b}{2a}## be ##\frac{b^2}{4a^2}## and not ##\frac{b^2}{4a}## as it is written in my textbook, I have also checked on the internet but the answer is the same, although I couldn't find why.

Thank you.

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