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Biblioteka

Exploration: The Shape of a Parabola

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Posljednje ažuriranje over 3 years ago
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The parabola in the graph of y = x^2 is concave up like an upward u . But if you threw a basketball then the parabola of the basketball’s trajectory is concave like a downward ∩

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Graph y = x2 + c for different values of c between 10 and +10.

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Use your findings to describe the similarities and differences in the shape of the graphs of each pair of quadratic functions.

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The standard form of a quadratic function is:

where a, b

and c are real numbers, and a ≠ 0.

IMPORTANT!!!!

You will need DESMOS to plot all the equations that are a part of this investigation. When using DESMOS, make sure you insert only the expression and not the entire equation.

For example, if I ask you to plot

then on DESMOS enter only

Also, note: In the previous class, I only marked absent the students who did absolutely no work. Today, I will be much stricter. I am not looking for exact answers, I am looking for sincere participation. If your Formatiev App is not working, take help from a friend and complete the task on a google doc. Share the doc with me at the end.

If you graph the quadratic function y = x2. The graph is a parabola as shown to the right.

Pitanje 1
1.

Go to DESMOS and Graph:

for a few values of a between 10 and +10.

Pitanje 2
2.

Find the values of a for which the parabola is concave up.

Pitanje 3
3.

Find the values of a for which the parabola is concave down.

Pitanje 4
4.

Find the values of a that make the parabola narrower than the graph

of y = x^2

Pitanje 5
5.

Find the values of a that make the parabola wider than the graph of y = x^2

Pitanje 6
6.

Describe the effects of changing the value of c.

Pitanje 7
7.

Graph y = x^2 + bx for different values of b between 10 and +10. Include

some non-integer values. Describe the effect of changing the value of b.

Pitanje 8
8.

Graph the linear function y = bx for different values of b. Describe how

the graph changes for different values of b

Pitanje 9
9.

Go back to the parabola y = ax^2 + bx. Give a any value except 0. Keep a fixed and change b. Describe how the shape of the parabola changes for different values of b

Pitanje 10
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Pitanje 11
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Pitanje 12
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