Exploring Quadratic Functions

1. A quadratic function is essentially just a parabola. A parabola is a curve that intersects at either the y-axis or x-axis, and then it mirrors itself on the other side. A quadratic equation is the equation that is used to plot parabolas. Unlike the slope y-intercept form, which has their equation as their name, a quadratic equation uses f(x) = ax^2+bx+c.

 

2. An example of a quadratic function is f(x) = ax^2+bx+c, an example of something not being a quadratic function is f(x) = x^3. This is not an example of a quadratic equation because the highest degree that a number could be is ^2.

 

3. If b and c are equal to 0, the parabola intersects right at 0. The symmetry happens once it intersects at 0, and then both sides mirror each other.

 

 

5.

When a<0, the graph has a maximum point of -2

When a>0, the graph has a minimum point of 3

When -1<a<1, the parabola opens down and it has a max point of (-4,0)

6. If the signs for a are positive, then the vertex has a minimum point, if it is negative, the vertex has a maximum point.

7. The vertex starts to shift vertically on the y-axis because of c changing constantly.

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