Graphing Quadratic Functions – Practice Problems

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The graph of a quadratic function f(x) = ax^2 + bx + c is a parabola, a symmetrical U-shaped curve which opens upwards when a is positive or downwards when a is negative.

To graph a parabola, first determine the maxima, or minima, of the parabola: the vertex (x,y) such that x = -b/2a and y = f(-b/2a). Plot this point in a (x,y)-coordinate system.

The axis of symmetry is the imaginary vertical line x = -b/2a that cuts the parabola in half. Plot two more points found on the right and left sides of the axis of symmetry which satisfy the given quadratic function.

Finally, connect these points with the vertex by drawing a smooth curve. The graph produced is a parabola.

Graph linear and quadratic functions and show intercepts, maxima and minima.


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Exercises in this Practice Problem
Describe how the coefficients change the graph.
Explain the change of the axis of symmetry depending on $a$ and $b$.
Determine the corresponding function.
Decide which function belongs to which graph.
Check the following statements.
Describe how to determine the vertex.