Question

Rewrite the function by completing the square. f(x)=x^2+x-30 It’s supposed to look like this f(x)= (x+ )^2+ .

Answer 1

Answer:

$f(x)=(x+1/2)^2 +(- 30.25)$

Step-by-step explanation:

In this question we are required to rewrite the given function by using completing the square method.

Completing the square method requires that our given equation can be written in form: $(a\pm b)^2 = a^2 \pm 2ab +b^2$

SO, we have to transform our equation according to above format.

Since our equation is $x^2+x-30$, we will transform it into

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

because the middle term of given equation has + sign.

$x^2+x-30=0\\x^2+x=30\\x^2 + 2(x)(1/2) + (1/2) ^2 = 30 + (1/2)^2$

We have introduced (1/2)^2 on both sides of the equation to gain the required form.

$(x+1/2)^2 = 30.25\\(x+1/2)^2 - 30.25 = 0\\f(x) = (x+1/2)^2 +(- 30.25)$

Our answer is $f(x)=(x+1/2)^2 +(- 30.25)$