6. 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 \( f(x+4) \), we substitute \( x+4 \) into the function \( f(x) = x^2 + 2x - 5 \). Here's the step-by-step process:<br /><br />### Step 1: Substitute \( x+4 \) into \( f(x) \)<br />\[<br />f(x+4) = (x+4)^2 + 2(x+4) - 5<br />\]<br /><br />### Step 2: Expand \( (x+4)^2 \)<br />\[<br />(x+4)^2 = x^2 + 8x + 16<br />\]<br /><br />So,<br />\[<br />f(x+4) = (x^2 + 8x + 16) + 2(x+4) - 5<br />\]<br /><br />### Step 3: Distribute \( 2(x+4) \)<br />\[<br />2(x+4) = 2x + 8<br />\]<br /><br />Now,<br />\[<br />f(x+4) = x^2 + 8x + 16 + 2x + 8 - 5<br />\]<br /><br />### Step 4: 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 />### Final Answer:<br />The correct option is:<br />\[<br />\boxed{c. \, x^2 + 10x + 19}<br />\]