1. A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape. Example: y= 2x^2+5x+6

 

2.

When A is 1 and everything else is zero it forms a parabola that has a minimum point of zero and is symmetrical. When B is 1 and everything else is zero it creates a 45 degree line ascending from left to right. When C is 1 and everything else is zero the forms a horizontal line that crosses y at 1.

 

3.

a)

The parabola is symmetrical and forms a u shape that goes through 2. When A is less than zero the parobala forms and upward facing bowl. When B is less than zero it is a diagonal line that goes up and to the left. When C is less than zero the graph becomes a horizontal line below zero

B)

When A is greater than zero the graph forms a upward facing bowl that has a minimum point of zero. When B is greater than zero it forms a diagonal line that goes ascends from left to right. When C is greater than zero the graph forms a horizontal line that crosses the y axis above zero.

C)

When A is greater than -1 but less than 1 the parabola gets wider because the value is closer to zero. When B is greater than -1 but less than 1 the diagonal line. When C is less than 1  but greater than -1 it gets closer to the y intercept of zero. The graph has a minimum point but no maximum

D)

When A is greater than 1 the parobala gets steeper cause its a higher value. When B is higher than 1 the diagonal gets steeper cause the value is higher. When C is greater than 1 the horizontal line gets higher because the value is greater. The graph gets steeper the higher the number and gets flatter the less the number for the A variable is

4. When A is positive the vertex is minimum, When A is Negative the vertex is maximum