Create a quadratic expression in standard form. b. Rewrite the expression by completing the square. Explain your work using com

Question

Create a quadratic expression in standard form.

b. Rewrite the expression by completing the square. Explain your work using complete sentences.

Use the order of operations to turn the expression back into standard form. Explain your work using complete sentences.

Explain why completing the square will always result in a perfect square trinomial.

PLEASE HELP ME!!! I ONLY HAVE SO MUCH TIME LEFT AND I REALLY NEED THIS!!! THIS IS WORTH 15 POINTS!!!!

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Aubrey 1 week 2021-11-25T09:38:00+00:00 1 Answer 0

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    2021-11-25T09:39:04+00:00

    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.

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