Q1 Graph the function and identify the domain and range y= -2x2
find the range
and domian
To graph the function y = -2x^2, we need to plot points on a coordinate plane.
We can start by selecting x-values and substituting them into the equation to find the corresponding y-values. For simplicity, let's choose an array of x-values such as -2, -1, 0, 1, and 2.
When x = -2, y = -2(-2)^2 = -2(4) = -8.
When x = -1, y = -2(-1)^2 = -2(1) = -2.
When x = 0, y = -2(0)^2 = -2(0) = 0.
When x = 1, y = -2(1)^2 = -2(1) = -2.
When x = 2, y = -2(2)^2 = -2(4) = -8.
These points (x, y) are (-2, -8), (-1, -2), (0, 0), (1, -2), and (2, -8).
Plotting these points on a graph and connecting them with a curve yields a downward-opening parabola that is symmetric about the y-axis.
The domain is the set of all possible x-values for the function y = -2x^2, which in this case is all real numbers.
The range is the set of all possible y-values for the function y = -2x^2. Since the coefficient of x^2 is negative, the graph is concave down, and the range will be all real numbers less than or equal to the y-coordinate of the vertex of the parabola.
To find the vertex, we utilize the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -2 and b = 0.
x = -0/(2(-2)) = 0/(4) = 0.
To find the y-coordinate of the vertex, we substitute the x-value back into the equation:
y = -2(0)^2 = -2(0) = 0.
Therefore, the vertex of the parabola is (0, 0).
Thus, the range is all real numbers less than or equal to 0, i.e., y ≤ 0.