Question

In what ways does adding a constant or coefficient to a quadratic equation affect the graph?

How are the axis of symmetry and vertex related?

What key features of a quadratic graph can be identified?

Answer 1

When you add a constant to a quadratic equation, the vertex of the graph will change depending on whether the constant is positive or negative.
When you add a coefficient to a quadratic equation, the graph will widen or narrow depending on whether the coefficient is positive or negative.
The axis of symmetry always passes through the vertex.
The key features of a quadratic graph are vertex, axis of symmetry, intercepts, focus, latus rectum, and directrix.

Answer 2

Answer with explanation:

Ques 1)

The quadratic equation is given by:

$y=a(x-h)^2+k$

                      Vertex is: (h,k)

Hence, on adding a simple constant the y-coordinate of the vertex gets changed , since there is a change in the term "k"

and adding a coefficient to the quadratic equation will change the graph in the manner that it could be wide or narrow depending on whether the coefficient is greater than 1 or less than 1 and also the sign of the coefficient describes whether the graph is open upward or downward.

Ques 2)

The axis of symmetry and the vertex are related in the manner that the axis of symmetry always passes through the vertex of the graph.

i.e. if the graph is a upward or downward open parabola then axis of symmetry is: y=k

and if the graph is a right or left open parabola then axis of symmetry is: x=h

where the vertex is: (h,k)

Ques 3)

The key features of a quadratic graph are:

1)   Vertex.

2)  Axis of symmetry.

3) x-intercept( also known as zeros)

4)  y-intercept.

5)  Focus

6)  Directrix.

7)  Latus Rectum.