QF - Graphing Quadratic Functions (Overview)


 

Graphing Quadratic Functions

Introduction

basketball.png Dribble, dribble, shoot, shoot, take that ball to the hoop hoop! When you shoot a basketball, how high does the ball go? Can you tell by the arc of the ball that it will go in? If you know how to graph quadratics and interpret their graphs, then you will know! In this module, we will take what we learned about solving quadratics, combine it with graphing and we will be able to analyze many different situations.

Essential Questions

  • How do I graph a quadratic function?
  • Where is the maximum or minimum of a quadratic function located?
  • What does the maximum or minimum of a quadratic function describe in the context of the problem?
  • How is the rate of change for a quadratic function different from the rate of change for a linear function?
  • How can the graph of f(x) = x2 move left, right, up, down, stretch, or compress?

Key Terms

The following key terms will help you understand the content in this module.

Axis of Symmetry - The vertical line that passes through the vertex splitting the parabola in half.

Horizontal Shift - A rigid transformation of a graph in a horizontal direction, either left or right.

Leading Coefficient - The first coefficient when a function is in standard form, usually referred to as "a".   This value determines if the parabola opens up or down.

Maximum Value - The greatest y-value the function reaches.

Minimum Value - The lowest y-value the function reaches.

Parabola - The shape a quadratic function makes.

Quadratic Function - A function of degree 2 which has a graph that "turns around" once, resembling an umbrella-like curve that faces either right-side-up or upside down. This graph is called a parabola.

Root - The x-values where the function has a value of zero.

Standard form of a quadratic function - f(x) = ax2 + bx + c

Vertex - The vertex is the maximum value of a parabola opening down or the minimum value of a parabolas opening up.

Vertex form of a quadratic function - The vertex form of a quadratic function is given by f(x) =a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

y-intercept - The point where the parabola crosses the y-axis.

x-intercept - The point where the parabola crosses the x-axis these represent the real solutions.

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