Question

Create a quadratic expression in standard form.

Answer 1

Answer:

Step-by-step explanation:

The quadratic expression in the standard form is given by :

f(x) = $ax^{2}$ + bx + c

(b) To complete the square:

Divide the equation through by a , the equation then becomes

f(x)= $x^{2}$ + $\frac{bx}{a}$ + $\frac{c}{a}$

At this point, you are require to

(i) multiply the coefficient of x by 1/2

(ii) square the result

(iii) add the result to both sides , we have

f(x) = $x^{2}$ + $\frac{bx}{a}$ + $(\frac{b}{2a}) ^{2}$ + $\frac{c}{a}$ + $(\frac{b}{2a}) ^{2}$by completing the square , we have

f(x) = $(x+\frac{b}{2a}) ^{2}$ + $\frac{c}{a}$ - $\frac{b^{2} }{4a^{2} }$ . We did this in order to make the expression balance

(c) Using the order of operation to turn the expression back into standard form

i. Expand the function in the bracket , we have

f(x) = $x^{2}$ + $\frac{bx}{a}$ + $(\frac{b}{2a} )^{2}$ + $\frac{c}{a}$ - $\frac{b^{2} }{4a^{2} }$

⇒ f(x) = $x^{2}$ + $\frac{bx}{a}$ + $(\frac{b}{2a} )^{2}$ + $\frac{c}{a}$ - $(\frac{b}{2a} )^{2}$

⇒f(x) =  $x^{2}$ + $\frac{bx}{a}$ + $\frac{c}{a}$

multiply through by the L.C.M , which is a , then we have

f(x) = $ax^{2}$ - bx + c .

Since the aim of completing the square is to make the expression a perfect square , then it will always result in a perfect square trinomial.