. If f(x)=x^2+2x-5 , evaluate f(x+4) a. x^2+2x+19 b. x^2+6x+11 c. x^2+10x+19 d. x^2+4x+29

To evaluate \( f(x+4) \) for the function \( f(x) = x^2 + 2x - 5 \), we need to substitute \( x+4 \) into the function in place of \( x \).<br /><br />1. Start with the original function:<br /> \[<br /> f(x) = x^2 + 2x - 5<br /> \]<br /><br />2. Substitute \( x+4 \) for \( x \):<br /> \[<br /> f(x+4) = (x+4)^2 + 2(x+4) - 5<br /> \]<br /><br />3. Expand \( (x+4)^2 \):<br /> \[<br /> (x+4)^2 = x^2 + 8x + 16<br /> \]<br /><br />4. Expand \( 2(x+4) \):<br /> \[<br /> 2(x+4) = 2x + 8<br /> \]<br /><br />5. Substitute these expansions back into the expression for \( f(x+4) \):<br /> \[<br /> f(x+4) = x^2 + 8x + 16 + 2x + 8 - 5<br /> \]<br /><br />6. Combine like terms:<br /> \[<br /> f(x+4) = x^2 + (8x + 2x) + (16 + 8 - 5)<br /> \]<br /> \[<br /> f(x+4) = x^2 + 10x + 19<br /> \]<br /><br />Therefore, the correct answer is:<br />c. \( x^2 + 10x + 19 \)