In this lesson, you will analyze the graphs of quadratic functions. In the first section, you will focus on the direction in which a parabola opens and the width of the parabola itself.

This is exciting! A smile is forming on your face.

The smile on your face could be considered a possible graph of a quadratic function. Click on the graph below.

• In which direction do both parabolas in the graph open?

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  Both parabolas open upward.

• What does the direction in which the parabolas tell you about the sign of the value of a in the function y = ax² that would generate each parabola?

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  Because both parabolas open upward, the sign of the value of a in the function generating each parabola is positive.

• How does the parabola representing the smile compare to the original parabola, which is the quadratic parent function, y = x²?

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  The parabola representing the smile is more narrow than the parent function.

• How does the value of a in the function y = ax² for the parabola representing the smile compare to the value of a for the parent function, y = x²?

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  The value of a for the parabola representing the smile is greater than 1 and is greater than the value of a for the parent function.

• Is the vertex for each parabola a minimum value or a maximum value? How can you tell?

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  The vertex for each parabola is a minimum value because the y-value for the vertex is less than the y-values for the remaining points on each parabola.