ewrite the function In standard form. (x)=3(x+4)^2-5 he standard form of f(x)=3(x+4)^2-5 f(x)= square square

To rewrite the function in standard form, we need to expand the expression inside the parentheses and simplify it.<br /><br />The given function is:<br />$f(x) = 3(x+4)^{2} - 5$<br /><br />Expanding the expression inside the parentheses:<br />$(x+4)^{2} = x^{2} + 8x + 16$<br /><br />Substituting this back into the function:<br />$f(x) = 3(x^{2} + 8x + 16) - 5$<br /><br />Simplifying the expression:<br />$f(x) = 3x^{2} + 24x + 48 - 5$<br /><br />Combining like terms:<br />$f(x) = 3x^{2} + 24x + 43$<br /><br />Therefore, the standard form of $f(x) = 3(x+4)^{2} - 5$ is:<br />$f(x) = 3x^{2} + 24x + 43$