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Complete the square to write the equation, 4x2 24x – y 43 = 0, in standard form. y = (x )2

User Coolhand
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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.

User Hrvoje Kusulja
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