This must be true for some value of x, since we have a quantity squared yielding a positive number, and since the equation is of second degree,there must exist 2 real roots.
Well he started off correct to the point of completing the square.
Answer:
They are represented by downward parabola
They have the same equations of line of symmetry
Their vertices have same x-coordinates but different y-coordinates
They have the same domains
They have different ranges
They have different maximum values at same x values
The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up
Step-by-step explanation:
y = -2x² is a quadratic equation which represents by a parabola
From the red graph:
The graph of y = -2x² is represented by downward parabola
It has a maximum vertex (0 , 0)
The line of symmetry at x = 0
Its maximum value = 0 at x = 0
Its domain is {x: x ∈ R}
Its range is {y: y ≤ 0}
From the blue graph:
The graph of y = -2x² + 4 is represented by down ward parabola
It has a maximum vertex (0 , 4)
The line of symmetry at x = 0
Its maximum value = 4 at x = 0
Its domain is {x: x ∈ R}
Its range is {y: y ≤ 4}
From the two graphs
They are represented by downward parabola
They have the same equations of line of symmetry
Their vertices have same x-coordinates but different y-coordinates
They have same domains
They have different ranges
They have different maximum values at same x values
The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up
