The standard form of the equation is:
[tex]x=8y^2-16y-7[/tex]
We know that the standard form of a quadratic equation is given by the expression:
[tex]x=ay^2+by+c[/tex]
where a,b and c are real numbers.
and a≠0
Here we are given the vertex form of the equation of a parabola by:
[tex]x=8(y-1)^2-15[/tex]
Now, on expanding the parentheses term by using the formula:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Here a=y and b= 1
Hence, we have:
[tex]x=8(y^2+1-2y)-15\\\\i.e.\\\\x=8\times y^2+8\times 1-2y\times 8-15\\\\i.e.\\\\x=8y^2+8-16y-15\\\\i.e.\\\\x=8y^2-16y+8-15[/tex]
( Since, in the last step we combined the constant term i.e. 8 and -15 )
Hence, we get the standard form of the equation as:
[tex]x=8y^2-16y-7[/tex]
