Katie is finding the standard form of the equations y = x2 + 6x + 4. What mistake did she make in her work? Show the correct answer.
Don't these have to be set equal to zero somehow?!
her mistake was she didn't add 2x+6x the correct answer is 2x+6x+4
2x+6x=8x so the equation will be
y=8x+4
To find the standard form of the equation y = x^2 + 6x + 4, we need to rewrite it in the form ax^2 + bx + c = 0. Katie's mistake might lie in how she grouped the terms. Let's go through the correct steps to find the standard form:
Step 1: Begin with the given equation: y = x^2 + 6x + 4.
Step 2: Rearrange the terms so that the equation is in the form ax^2 + bx + c = 0. In this case, subtract y from both sides:
y - y = x^2 + 6x + 4 - y.
This gives us: 0 = x^2 + 6x + 4 - y.
Step 3: We want the leading coefficient (the coefficient of x^2) to be positive, so if necessary, multiply the entire equation by -1. In this case, we don't need to do that because the leading coefficient is already positive.
Step 4: Reorder the terms to arrange them in standard form:
0 = x^2 + 6x - y + 4.
In the equation above, the coefficient of x^2 is 1, the coefficient of x is 6, the constant term (c) is -y + 4.
Therefore, the correct standard form of the equation y = x^2 + 6x + 4 is:
0 = x^2 + 6x - y + 4.