Complete the square to re-write the quadratic function in vertex form:
y, equals, minus, 3, x, squared, minus, 18, x, minus, 26
y=−3x
2
−18x−26
To complete the square for the given quadratic function, we need to rearrange the equation and add a constant term to both sides.
Starting with the equation:
y = -3x^2 - 18x - 26
Let's focus on the terms involving x:
-3x^2 - 18x
To complete the square for this part, we need to take half of the coefficient of x (-18) and square it. Half of -18 is -9, and squaring it gives us 81. So, we need to add 81 to both sides:
y + 81 = -3x^2 - 18x + 81
Now, let's rearrange the terms in the right side to create a perfect square trinomial:
y + 81 = -3(x^2 + 6x) + 81
To create a perfect square trinomial inside the parentheses, we need to take half of the coefficient of x (6) and square it. Half of 6 is 3, and squaring it gives us 9. So, we need to add 9 inside the parentheses:
y + 81 = -3(x^2 + 6x + 9) + 81
Now, the equation can be rewritten as:
y + 81 = -3(x + 3)^2 + 81
Finally, we can simplify it further by subtracting 81 from both sides to isolate y:
y = -3(x + 3)^2 + 0
Thus, the quadratic function in vertex form is:
y = -3(x + 3)^2