Question

Rewrite the function by completing the square. f(x)= x^{2} + x -30f(x)=x 2 +x−30f, left parenthesis, x, right parenthesis, equals, x, squared, plus, x, minus, 30 f(x)=f(x)=f, left parenthesis, x, right parenthesis, equals (x+(x+left parenthesis, x, plus )^2+) 2 +right parenthesis, squared, plus

Answer 1

Answer:

$f(x)= (x+\frac{1}{2} )^{2}-30\frac{1}{4}$

Step-by-step explanation:

$f(x)= x^{2} + x -30$

To re-write the function by completing the square, the procedure is to first

(i)take the coefficient of x

(ii)Divide it by 2 and Square it

Coefficient of x=1

Divided by 2 = 1/2

Square of 1/2 = $(\frac{1}{2} )^{2}$

Next, we add it to the function and subtract same so that the equation remains balanced

$f(x)= x^{2} + x +(\frac{1}{2} )^{2}-(\frac{1}{2} )^{2}-30$

Pick each of the squared term and square the sum

$f(x)= (x+\frac{1}{2} )^{2}-(\frac{1}{2} )^{2}-30$

$f(x)= (x+\frac{1}{2} )^{2}-30\frac{1}{4}$