Question

The quadratic function below in standard form y= -6(x - 3)2 -9

Answer 1

The quadratic function y=-6(x-3)2-9 is in standard form which is written as y=ax2+bx+c. In this form, the coefficient x2(a) is -6, the coefficient of x(b) is 0 (since there is no x term),and the constant term (c) is -a.

1. The vertex form of a quadratic function is give by y=a(x-h)2+k, where (h,k) represent is the coordinates of the vertex form of the function is y=-6(x-3)2-9.from this form, we can identify that the parabola these represents a horizontal shift of the parabola, and the "-9" outside the parentheses represents a vertical shift .
2. The coefficient of x2 (a) determines the shape of the parabola. In this case, since a is negative (-6) the parabola opens downwards.
3. The term inside the parabola (x-b)-a horizontal shift of the parabola. In this case, the parabola is shifteds units to the right
4. The constant term (-a) is a vertical shift of the parabola. In this case the parabola is shifted a units downwards.

. To graph this quadratic function, start by plotting the vertex at (3,-9). Then, use the shape determined by the coefficient to x2(-6) the downwards opening parabola. The horizontal and vertical shift will determine the position of the parabola on the coordinate plane.