If we express −2x2+4x+5 in the form a(x−h)2+k, then what is k?
Solution — click to reveal
We complete the square. First, we factor −2 out of the terms −2x2+4x to get −2(x2−2x). We can square x−1 to get x2−2x+1, so −2(x2−2x)=−2[(x−1)2−1]=−2(x−1)2+2, and −2(x2−2x)+5=−2(x−1)2+2+5=−2(x−1)2+7.We see that k=7.