graphing quadratic functions

Basics of Graphing Quadratic Functionsadapted from hisema01

What is a Quadratic Function?

A function with the form y = ax2 + bx + c where a 0.

The graph is U-shaped and is called a parabola.

Why Study Quadratics?

Many things we see every day are modeled by quadratic functions.

What are some examples? Water in a drinking fountain

The McDonald’s Golden Arches

The path of a basketball

Quadratic Vocab The lowest or highest point is called the vertex.

The axis of symmetry is a vertical line through the vertex.

Effects of “a” Standard Form: y = ax2 + bx + c

Just like with absolute value functions: If a > 0 (+), the parabola opens up

If a < 0 (-), the parabola opens down

Effects of “a” Standard Form: y = ax2 + bx + c

Just like with absolute value functions:

If |a| < 1, the parabola is wider than y = x2

because it’s vertically shrunk

If |a| > 1, the parabola is narrower than y = x2 because it’s vertically stretched.

Effects of “c”

Standard Form: y = ax2 + bx + c

Just like with absolute value functions:

If c < 1, the parabola is shifted down c units

If c > 1, the parabola is shifted up c units

Finding the Vertex The x-coordinate of the vertex is

To find the y, plug the x-coordinate into the equation.

Axis of symmetry is the line x =

Graphing in Standard Form1. Find and plot the vertex:

2. Draw the axis of symmetry: x = 2

Example:y = 2x2 – 8x + 6

Graphing in Standard Form3. Choose two x values on one side and plot the points. x y 3 0 4 64. Use symmetry to plot two points on the other side.

5. Lastly, you should connect the points with a curve (parabola).

Example:y = 2x2 – 8x + 6