quickclick330 said:okay so completing the square gives me
y = x^2 +8x + 20 + 16 - 16
y = (x^2 + 8x +16) + 4
then factor...
y = (x + 4)^2 + 4
which is exactly what I got before?
The standard form of a parabola is y = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. This form is also known as the quadratic form.
The term a represents the coefficient of the squared term, b represents the coefficient of the linear term, and c represents the constant term. These values determine the shape, direction, and position of the parabola.
If a is positive, the parabola opens upwards and has a minimum point. If a is negative, the parabola opens downwards and has a maximum point. The value of a also affects the steepness of the curve.
Yes, the standard form can be used to graph any parabola. By substituting different values for a, b, and c, you can create different parabolas with varying shapes and positions.
The standard form can be rewritten as y = a(x - h)^2 + k, where h and k represent the coordinates of the vertex. This form is known as the vertex form and can be used to easily find the vertex of a parabola.