The standard form is:
[tex]y=ax^2+bx+c[/tex]
To get it from the vertex form we need to do the operations and simplify like terms. With this in mind we have:
a.
[tex]\begin{gathered} y=(x+5)^2+4 \\ y=x^2+10x+25+4 \\ y=x^2+10x+29 \end{gathered}[/tex]
Therefore the standard form is:
[tex]y=x^2+10x+29[/tex]
b.
[tex]\begin{gathered} y=2(x-7)^2-8 \\ y=2(x^2-14x+49)-8 \\ y=2x^2-28x+98-8 \\ y=2x^2-28x+90 \end{gathered}[/tex]
Therefore the standard form is:
[tex]y=2x^2-28x+90[/tex]
c.
[tex]\begin{gathered} y=-3(x+4)^2+1 \\ y=-3(x^2+8x+16)+1 \\ y=-3x^2-24x-48+1 \\ y=-3x^2-24x-47 \end{gathered}[/tex]
Therefore the standard form is:
[tex]y=-3x^2-24x-47[/tex]
d.
[tex]\begin{gathered} y=0.5(x-3)^2-4.5 \\ y=0.5(x^2-6x+9)-4.5 \\ y=0.5x^2-3x+4.5-4.5 \\ y=0.5x^2-3x \end{gathered}[/tex]
Therefore the standard form is:
[tex]y=0.5x^2-3x[/tex]
