# Quadratic Formula

PLEASE SHOW ALL WORK RELEVANT TO EACH ANSWER.

**ANSWERS WITHOUT JUSTIFICATION WILL NOT RECEIVE CREDIT.**

Please provide your justifications in paragraph form using full sentences.

Each problem is worth 10 points.

Please do not attempt to justify your answers by “plugging in” numbers . Use

variables and algebraic reasoning .

1) a) Use the quadratic formula to demonstrate algebraically that the

roots of ax ^2 + bx + c = 0 are the same as the roots of

kax^2 + kbx + kc = 0.

b) Give a particular example of this phenomenon.

c) Explain what this means in terms of solving equations of the form

kax^2 + kbx + kc =0 .

2) By the quadratic formula , the roots of a quadratic equation of the form

ax^2 + bx + c = 0 are given by

Demonstrate algebraically that

and that

Explain your reasoning in paragraph form.

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