Question

What key features of a quadratic graph can be identified, and how are the graphs affected when constants or coefficients are added to the parent quadratic equations?

Answer 1

We have that the parent function of a quadratic graph is

`f(x)=x^2`

The graph of a quadratic graph is always a parabola

The parts of a parabola are

• Vertex

,

• Axis of symmetry

,

• Latus rectum

,

• Focus

,

• Directrix

,

• y-intercept

,

• x-intercept

The graph can be affected:

If we add a positive number to the x-variable, then the graph will move to the left.

If we add a negative number to the x-variable, then the graph will move to the right.

If we add a positive number to the function, then the graph will move upwards.

If we add a negative number to the function, then the graph will move downwards.

If we multiply -1 to the x- variable we will have a reflection over the y-axis

If we multiply -1 to the function we will have a reflection over the x-axis

if we multiply a number between 0 and 1 to the x-variable we will have a horizontal stretch

if we multiply a number greater than 1 to the x- variable we will have a horizontal compression

if we multiply a number between 0 and 1 to the function we will have a vertical compression

if we multiply a number greater than 1 to the function we will have a vertical stretch