What are Quadratic Functions? – Practice Problems

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A quadratic function is represented by the standard form, y = ax2 + bx + c.

In order for such an equation to be a quadratic function, and not a linear one, we must have that the coefficient a is not equal to zero; i.e. a ≠ 0.

The graph of a quadratic function is a parabola. The larger the absolute value of a is, the thinner the shape of the parabola becomes. The smaller the absolute value, the wider the parabola becomes.

The coefficient a is also an indicator of the direction of the shape of the parabola. If the value of a is positive, the parabola opens upwards. If the value of a is negative, the parabola opens downwards.

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

CCSS.MATH.CONTENT.HSF.IF.C.7.A

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Exercises in this Practice Problem
Decide if the given shape is a parabola.
Describe a quadratic function and the role of $a$.
Identify the value of the coefficient $a$ of each parabola.
Find the corresponding quadratic function.
Determine which functions are quadratic functions.
Explain how to find the corresponding quadratic function.