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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