1. A quadratic equation is used in at least one variable and the highest-degree term is the same as the second degree.

2. Give an example of a quadratic function and give an example of a function that is NOT a quadratic.

An example of a quadratic function is and an example of a function that isn’t a quadratic is y= 2x + 1

3. Either side of the parabola is completely the same but the x values are opposites.  What I mean by this is, if one of the sides of the curve is crossing the point (1,1) for example, then the other side crosses the point (-1,1)

4. The functions I chose to compare were and These two functions have several differences to them. First, the graph that shows ‘s curve turns quicker so it’s therefore skinnier and it starts on a y intercept point less than 2 on the graph so that means that it’s longer as well. Also, it’s x intercept for the tip of the parabola is a number smaller than one but bigger that zero. The other function ()‘s curve starts on the coordinates (1,2) and is much wider of a curve.

5. a) a < 0: I used -1 < 0. The parabola flipped upside down and now the y value is negative for each point.
i.  The maximum point of this graph is -1.
b) a > 0: I used 1 > 0. The parabola became skinnier, meaning that the possibilities for x values diminished.
i. The minimum point on the graph is 1.
c) -1 < a < 1: If the a value is 0, it becomes a straight line that runs along the x axis with a y value of 0 forever.
d) a > 1 OR a < -1: The parabola flipped over again when I made a = -3 and it’s even skinnier of a curve than it was before. Also, the centre of the curve is on (0,0).

6. We call the maximum or minimum point of a quadratic function the vertex. Make two statements that describes the relationship between the sign of (positive and negative) and whether the vertex is a maximum or minimum.

The vertex for this parabola () is a maximum at 6. You can tell because the parabola is negative since the curve goes down. Also, the numbers become smaller and more negative.

7. When c changes, the point that the curve starts at gets higher or lower depending on the y axis number.

Part 2:
Roots are the solutions to the quadratic equation. The roots are found by looking at where the curve crosses the x axis (x-intercepts).

See if by adjusting the sliders, you can get a curve that just touches the x axis (y=0). ***

Equation: ________________________________

This quadratic equation has ONE solution.

To get the roots 1 and -1:

Equation:

This quadratic equation has TWO solutions.

To get the curve not to cross the x-axis:

Equation:  

When the curve does NOT cross the x-axis, there are NO REAL solutions for this equation.