Rewrite the function by completing the square. {:[f(x)=x^(2)-8x-51],[f(x)=(x+◻)^(2)+◻]:}

Question

Rewrite the function by completing the square.  {:[f(x)=x^(2)-8x-51],[f(x)=(x+◻)^(2)+◻]:}

Bytelearn · Accepted Answer

Identify Coefficients: Identify the quadratic and linear coefficients from the given quadratic function. The quadratic function is given as f(x) = x^2 - 8x - 51. Here, the quadratic coefficient is 1 (the coefficient of x^2) and the linear coefficient is -8 (the coefficient of x).Complete the Square: Divide the linear coefficient by 2 and square the result to find the number to complete the square. The linear coefficient is -8, so we divide it by 2 to get -4. Squaring -4 gives us (-4)^2 = 16. This is the number we will add and subtract inside the parentheses to complete the square.Rewrite the Function: Rewrite the function by adding and subtracting the number found in Step 2 inside the parentheses. We add and subtract 16 to the function f(x) = x^2 - 8x - 51 to complete the square. This gives us f(x) = (x^2 - 8x + 16) - 16 - 51.Factor the Quadratic Expression: Factor the quadratic expression inside the parentheses. The quadratic expression x^2 - 8x + 16 can be factored into (x - 4)^2 because (x - 4)(x - 4) = x^2 - 8x + 16.Combine the Constants: Combine the constants outside the parentheses. We have -16 - 51 outside the parentheses, which combines to -67. So the function now reads f(x) = (x - 4)^2 - 67.Final Form of the Function: Write the final form of the function after completing the square. The function after completing the square is f(x) = (x - 4)^2 - 67.

Rewrite the function by completing the square. $\newline$ $f(x) = x^2 - 8x - 51$ , $f(x) = (x + \square)^2 + \square$

Full solution

More problems from Solve a quadratic equation by completing the square

Related topics

Rewrite the function by completing the square.\newlinef(x)=x2−8x−51 f(x) = x^2 - 8x - 51 f(x)=x2−8x−51, f(x)=(x+□)2+□ f(x) = (x + \square)^2 + \square f(x)=(x+□)2+□

Rewrite the function by completing the square. $\newline$ $f(x) = x^2 - 8x - 51$ , $f(x) = (x + \square)^2 + \square$