1. Quadratic Functions

2. A quadratic function is a nonlinear function that can be written in standard from y = ax2 + bx + c
The U-Shaped graph of a quadratic function is called a parabola
The parent function of a quadratic function is y=x2
The highest or lowest point on a parabola is the vertex. Therefore, the minimum or maximum value of a quadratic function occurs at the vertex.

4. End Behavior of a Graph Given a quadratic function in the form
𝒇 𝒙 =𝒂 𝒙 𝟐 + bx + c
Standard form
𝒇 𝒙 =𝒂 𝒙 −𝒉 𝟐
Vertex Form
Quadratic function is said to open up if a > 0 and open down if a < 0.

5. The minimum value of a function is the least possible y-value for that function.
If a > 0 then f has a minimum at the x -coordinate of the vertex,
The maximum value of a function is the greatest possible y-value for that function.
If a < 0 then has a maximum at x-coordinate of the vertex

7. Review Domain is all the possible x values of a function
From left to right
Range is all the possibly y values of a function
From bottom to top

8. Unless a specific domain is given, the domain of a quadratic function is all real numbers.
One way to find the range of a quadratic function is by looking at its graph.

9. Roots Vs Solutions Roots are solutions to a one variable equations.
So roots and solutions are synonymous.
Zeroes indicate you are looking at a graph and a 2 variable equation.
They are the x-values where y = 0.
Imaginary roots cannot be located on a rectangular on a graph

10. Two Solutions
A quadratic equation has two solutions if the graph of its related function has two x-intercepts
Would have 2 real roots and 2 zeroes

11. One Solution
A quadratic equation has one solution if the graph of its related function has one x-intercept
One zero and a double real root

12. No Real Solutions
A quadratic equation has no real solution if the graph of its related function has no x-intercepts
No zeroes but 2 non real roots

13. State the vertex, the solutions, the domain and the range of each

14. State the vertex, the solutions, the domain and the range of each