(x+1)²- 8
1) Considering the equation 2x²+4x-6, and that in the expression (x-h)²+k
we have:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=\frac{-\Delta}{4a} \end{gathered}[/tex]2) Then, let's find out h and k the values of the vertex of that quadratic function:
[tex]\begin{gathered} h=\frac{-4}{2(2)}=\frac{-4}{4}=-1 \\ k=\frac{-\Delta}{4(2)}=\frac{-(4^2-4(2)(-6))}{8}=\frac{-64}{8}=-8 \end{gathered}[/tex]So the vertex is (-1, -8). Plugging into that 2nd expression, we'll have an equivalent one:
[tex](x-(-1)^2+(-8)\text{ }\Rightarrow(x+1)^2-8[/tex]3) So the equivalent expression to that quadratic equation is (x+1)²-8
