graph y=-2x^2+7 on your paper. find domain and range

Question

please help

Answer 1

Y = 2x²+ 7

When equation is in the form of y = Ax2 + Bx + C, it is in standard form.

A = 2, B = 0

Since A is positive, the graph opens upward.
Vertex is the lowest point on the graph.
The x coordinate of the vertex occurs at -B/2A

X =-B/2A = -0/2(2) = 0

To find the y-coordinate, we substitute 0 and solve for y

Y = 2(0)² + 7 = 7

The vertex is at (0,7) ... the lowest point on the graph

From here, you can construct a table of values for x, and solve for y to obtain points on the graph.

Good x values to pick are -2, -1, 1, and 2

The domain is all the x-values for which the function is defined, The function is defined for all real values of x.
The domain is all real numbers. { x | x is a real number }

The range is all the y values obtained from input of the x-values.
The smallest y value is 7, the largest is positive infinity.
The range is all real numbers ≥ 7. { y | y ≥ 7 }