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Quadratic Function: Vertex, Symmetry and Maximum/Minimum Value

For each quadratic function find:
a. the vertex
b. the line of symmetry
c. the maximum or minimum value

Then graph the function. Please show your work.

y = -4x^2 - 7x + 2

Please see the attached file for the fully formatted problems.


Solution Preview

First, I would rearrange the equation into the "standard form", from which the information can be easily read.

The graph of a quadratic function is a parabola. By completing the square on x it is possible to write the equation for a parabola in the form:
(x-k)^2 = 4p(y-h)

and then the point (h, k) is the vertex of the parabola.

Your equation is y = -4x^2 - 7x + 2

Look at the terms that contain x: -4x^2 - 7x. To complete the square, it is best to take out a factor of -4, so you have -4(x^2+(7/4)x).

Now recall that a "perfect square" is a quadratic that, when ...

Solution Summary

The Vertex, Symmetry and Maximum/Minimum Value are found for a quadratic equation.