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
2
()
gxaxbxc
=++
(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).
Worksheet 5.5
Three Formulas for a Quadratic Function
g(x
)
vertex form: g(x) = _____________________________
standard form: g(x) = ___________________________
factored form: g(x) = ____________________________
