Final answer:
To write the equation 4x^2 + 24x - y - 43 = 0 in standard form by completing the square, we can follow these steps:
Step-by-step explanation:
To write the equation 4x^2 + 24x - y - 43 = 0 in standard form by completing the square, we need to rearrange the equation so that it has the form (x - h)^2 = k, where (h, k) is the vertex. Here's how we can do it:
Step 1: Move the constant term to the right side of the equation: 4x^2 + 24x - y = 43
Step 2: Complete the square for the coefficient of x^2: Divide the coefficient of x by 2 and square it. Add the square to both sides of the equation:
4x^2 + 24x + (24/2)^2 = y + 43 + (24/2)^2
Step 3: Simplify the right side of the equation: 4x^2 + 24x + 144 = y + 67
Step 4: Write the left side of the equation as a perfect square: (2x + 6)^2 = y + 67
So, the equation in standard form is y = (2x + 6)^2 - 67.