Lesson 4 of 5
Use a quadratic to connect a context, vertex, intercepts, and sensible inputs.
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Worked example · 1 of 8
Worked example
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For , name the vertex and opening direction. Check: vertex , opening downward.
Big ideas
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A quadratic model has a nonzero squared-term coefficient. Standard form shows the starting output c when input 0 is allowed.
In vertex form , the vertex is . For standard form, and . State what both coordinates mean.
The zeros solve . A positive height model may have a mathematical negative-time root; reject that root when time starts at 0.
State units and a context domain. Predictions describe the supplied model only within its stated situation; a formula alone does not establish physical accuracy.
Worked example
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A fictional height is . Factor to ; positive ground contact is at 6. Complete the square to ; the maximum height is 16 at time 2, inside the physical flight interval.
Step-through
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A toy glider height model is metres, from launch until landing. Find the maximum height and landing time.
Whole picture, 4 steps
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Worked example
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A rectangle has perimeter 28 cm. If width is w cm, length is cm. Area . For positive side lengths, . The largest area is 49 square cm when both sides are 7 cm.
Worked example
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A model has vertex and passes through . Write . Substitute : , so . Thus . Check: at the model returns 1.
Mix-up alert
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Wrong idea: a vertex at means the maximum occurs at 18 seconds. Repair: the first coordinate is the input and the second is the output. For a downward height model, maximum height is 18 m at 4 s.
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Flashcards
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Card 1 of 8
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Evaluate h(0).
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What does c represent in when is launch?
The height at launch.
Where is the vertex input for ?
.
Does give a maximum or minimum on all real inputs?
A maximum.
How do you find when a height model reaches the ground?
Set height equal to zero and check permitted times.
Why might you reject a negative-time root?
The model may be restricted to times at or after launch.
What is the area unit for side lengths in metres?
Square metres, .
Which form makes the vertex visible?
.
How do you determine a from vertex and another point?
Substitute the point into and solve for a.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
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Write it
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Write it
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Start here if it helps: I can connect the conditions by...
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Connect the ideas
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