IDENTIFYING CHARACTERISTICS OF QUADRATIC FUNCTIONS A quadratic function is a nonlinear function that can be written in the standard form y = ax 2 + bx + c, where a ≠ 0. The U-shaped graph of a quadratic function is called a parabola. In this lesson, you will graph quadratic functions, where b and c equal 0.

CHARACTERISTICS OF QUADRATIC FUNCTIONS

EXAMPLE 1 – IDENTIFYING CHARACTERISTICS OF A QUADRATIC FUNCTION You can also determine the following: The domain is all real numbers. The range is all real numbers greater than or equal to −2. When x < −1, y increases as x decreases. When x > −1, y increases as x increases.

IDENTIFY CHARACTERISTICS OF THE QUADRATIC FUNCTION AND ITS GRAPH. The vertex is (2, −3). The axis of symmetry is x = 2. The domain is all real numbers. The range is y ≥ −3. When x < 2, y increases as x decreases. When x > 2, y increases as x increases. The vertex is (−3, 7). The axis of symmetry is x = −3. The domain is all real numbers. The range is y ≤ 7. When x < −3, y decreases as x decreases. When x > −3, y decreases as x increases.

When a is positive, the shape looks like a U. When a is between 0 and 1, the graph is a vertical shrink. (looks wider) When a is greater than 1, the graph is a vertical stretch. (looks thinner)

Both graphs open up and have the same vertex, (0, 0), and the same axis of symmetry, x = 0. The graph of g is narrower than the graph of f because the graph of g is a vertical stretch by a factor of 2 of the graph of f.

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EXAMPLE 4 - SOLVING A REAL-LIFE PROBLEM

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