Question

Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs
Have tried to understand this, all I know is after finding the position for -2x^2, the -2x^2+4 will just move upwards by 4.
Real answers please :)

Answer 1

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