With methods

Foreword

Using the formula

\(a^2-2ab+b^2=a^2-2ab+(-b)^2=(a-b)^2\)

\(a^2+2ab+b^2=(a+b)^2\)

Remarks

Case The quadratic formula: \ (F (X) = - ^ 2 + 2x + 5X. 3 \)

Analysis: \ (F (X) = - ^ 2 + 2x + 5X. 3 = -2 (X ^ 2- \ cfrac. 5} {2} {X) +3 \)

\(=-2(x^2-\cfrac{5}{2}x+\triangle )+3+2\triangle\)

\(=-2[x^2-\cfrac{5}{2}x+(-\cfrac{5}{4})^2]+3+2\times(-\cfrac{5}{4})^2\)

\(=-2(x-\cfrac{5}{4})^2+\cfrac{49}{8}\)

• With the method steps

The corresponding exercises

Practice 1 The quadratic formula: \ (F (X) = - ^ 2 + 2x-3x 2 = -2 (X-\ cfrac. 3 {} {}. 4) ^ 2- \ cfrac. 8} {}. 7 {\) ;

Practice 2 The quadratic formula: \ (F (X) = ^ 2 + 3x-6X. 3. 1 = (X +. 1) 2-4 ^ \) ;

Practice 3 The quadratic formula: \ (F (X) = \ {cfrac. 4. 3} {X} ^ 2-2x = \. 3 cfrac {} {}. 4 (X-\. 4 cfrac {} {}. 3) ^ 2- \. 4 cfrac {} {}. 3 \) ;