y=x2+6

y/x+8

y=8x

Y=X^2 + 6. This the Eq of a Y-parabola

that opens upward.

h = Xv = -b/2a = 0/2 = 0.

k = Yv = 0^2 + 6 = 6.

V(h, k) = V(0, 6).

X = (-b +- sqrt(b^2 - 4ac)) / 2a,
X = (0 +- sqrt(0 - 24) / 2,
X = +- sqrt(4*6*-1),
X = +-2i*sqrt(6) = 2 imaginary solutions.

There are no real solutions, because
the graph does not cross or touch the
X-axis.

The equation y = x^2 + 6 represents a quadratic function. In this function, the variable x represents the input or independent variable, and y represents the output or dependent variable.

If you want to find specific values of y for given values of x, you can substitute those x values into the equation and calculate the corresponding y values. For example, if you want to find the value of y when x is 3, you can substitute x = 3 into the equation:

y = (3)^2 + 6
= 9 + 6
= 15

So, when x = 3, y = 15.

To explore the behavior of the function and see how the values of y change with different values of x, you can create a table of values or plot the graph of the function on a coordinate plane. This will allow you to visualize the relationship between x and y and identify any patterns or characteristics of the function.

The general shape of the graph of a quadratic function is a parabola. In this case, the coefficient in front of the x^2 term is positive (1), which means the parabola opens upwards. The constant term (6) determines the vertical shift of the parabola.

By analyzing the graph or table of values, you can determine other properties of the function, such as the x- and y-intercepts, vertex, and whether the function reaches a maximum or minimum point.