Write the function in standard form. f(x)=-5(x-8)^2+11 f(x)=square (Simplify your answer.Use integers or decimals for any numbers in the expression

To write the function \( f(x) = -5(x-8)^2 + 11 \) in standard form, we need to expand the expression and simplify it.<br /><br />Start by expanding the squared term:<br /><br />\[<br />(x-8)^2 = (x-8)(x-8) = x^2 - 16x + 64<br />\]<br /><br />Now substitute this back into the function:<br /><br />\[<br />f(x) = -5(x^2 - 16x + 64) + 11<br />\]<br /><br />Distribute the \(-5\) across the terms inside the parentheses:<br /><br />\[<br />f(x) = -5x^2 + 80x - 320 + 11<br />\]<br /><br />Combine the constant terms:<br /><br />\[<br />f(x) = -5x^2 + 80x - 309<br />\]<br /><br />Thus, the function in standard form is:<br /><br />\[<br />f(x) = -5x^2 + 80x - 309<br />\]