Exploring Quadratic Functions

1. Definition: A quadratic function is the degree of 2. Can be written in this form ( y = a$x^2$ + bx + c)
graph of every quadratic function is called a parabola.

2. examples

a) function with:

b) function without:

3. desmos

a) see what happens:
graph forms a dip like thing on the graph. when you move the slider it changes in width, length and height.

b) Start with slider values a=1,b=0,c=0. Describe any symmetry you notice:
This turned the graph to be exactly center on the 0 line on the graph. Everything looked organized and perfectly lined up.

4. Compare two functions:
x² + 7x + 12 = 0
find two numbers which come to 7 and multiply to be 12. You immediately come up with (3, 4). which would be both your x values.

5. Describe what happens to the graph when:

a) a<0 Does the graph have a maximum point or a minimum point? - no? b) a>0
Does the graph have a maximum point or minimum point?
– no?

c) -11 or a<-1 - i still dont know 6. Make two statements that describes the relationship between the sign of a (positive and negative) and whether the vertex is a maximum or minimum: a) im still very confused by this b) same here 7. ?