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Three Formulas for a Quadratic Function

The function g(x) shown in the graph is a translation of f(x) = 2x2.

1. Find a formula for g (x) using the fact that it is
a translation of f(x) = 2x2.
Tip: Check with a grapher .

2. Simplify the formula for g(x) so that it has the form
g(x) = ax2 + bx + c (standard form).
Tip: Check with a grapher .

3. g(x) is a quadratic function that can be factored.
Write down the formula in factored form .
Tip: Check with a grapher

4. Use the graph to find the coordinates of the vertex of g (x). _____________________
Is there a connection between the coordinates of the vertex and the formula in Question 1?
Explain.

5. Use the graph to find where g(x) crosses the y-axis. _______________
Is there a connection between the y- intercept and the formula in Question 2? Explain.

6. Use the graph to find where g(x) crosses the x-axis. ________________
Is there a connection between the zeros (x-intercepts) and the formula in Question 3?
Explain.

7. Write down three different formulas for g(x).

vertex form : g(x) = _____________________________

standard form: g(x) = ___________________________

factored form : g(x) = ____________________________

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