Valerie Russell
Exploring a
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Let's see what happens as a increases or decreases.
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As a increases the parabola stretches creating a narrower parabola |
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Likewise, as a decreases the parabola shrinks creating a broader parabola. |
So far we have seen that if the leading coefficient a is positive the quadratic function called a parabola opens upward and if the leading coefficient is negative the parabola opens downward. As a increases the parabola stretches and as a decreases the parabola shrinks.
Exploring b
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Exploring c
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Notice that as c increases the parabola moves upward. As c decreases the parabola moves downward.
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Did you know that you can easily see where the vertex and axis of symmetry lie in a quadratic equation when it is in vertex form? You can change the standard form of a quadratic equation to vertex form by using a method called completing the square. Let's take a look at several quadratic equations in vertex form.
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The coefficient of the quadratic equation a causes the parabola to shrink as a decreases and stretch vertically as a increases. |
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Extensions:
Adding xy to the first equation allows us to see the parabolas in space. In both cases the parabolas are moved down 1 unit. |
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