Solving Quadratic Equations by Completing the Square – Practice Problems

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One of the most effective methods of solving a quadratic equation is by completing the square. It is also the method that makes it easiest to graph the equation as well.

By completing the square, we can find, not only the roots of the equation, but also the vertex of the graph of the equation. This is because we will pass from the standard form, ax^2 + bx + c = 0, to the vertex form, a (x - h)^2 + k = 0, with (h,k) as the vertex of the graph.

The steps of this method must be taken carefully, though. The standard form must be gradually solved to arrive at the vertex form:
1. Finding the value that needs to be added on both sides of the equation to complete the square;
2. Finding the square roots of both sides of the equation;
3. Finding the roots of the equation by finally solving for x using the positive and negative values of the square root of the right side.

In this video, the method of completing the square to solve an equation and plotting its graph is explained.

Analyze Functions Using Different Representations.


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Exercises in this Practice Problem
Determine the vertex of the parabola.
Find the zeroes of the quadratic equation.
Solve for the zeroes of each quadratic equation.
Calculate the vertex and zeroes of the quadratic equation.
Identify the vertex form of a quadratic function.
Identify the graphs of the functions.