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 and rewrite the quadratic function in vertex form, we need to manipulate the equation to be in the form y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
1. Start by factoring out the common factor of -3 from the terms involving x^2 and x:
y = -3(x^2 + 6x) - 26
2. To complete the square, take half of the coefficient of the x term (6) and square it: (6/2)^2 = 9. Add this value inside the parentheses, but since you added it inside the parentheses, you also need to subtract it outside to maintain the original equation:
y = -3(x^2 + 6x + 9 - 9) - 26
3. Simplify the equation inside the parentheses:
y = -3((x + 3)^2 - 9) - 26
4. Distribute the -3 to both the terms inside the parentheses and the "-9" term outside the parentheses:
y = -3(x + 3)^2 + 27 - 26
5. Combine like terms:
y = -3(x + 3)^2 + 1
The quadratic function y = -3x^2 - 18x - 26 can be rewritten in vertex form as y = -3(x + 3)^2 + 1. The vertex of this parabola is (-3, 1).