Graphing Functions: Completing the Square, Quadratic Functions, Axis of Symmetry, and Intercepts

1. Using completing the square to describe the graph of the following function. Support your answer graphically.
f(x) = -2x^2 + 4x + 1
2. Graph the function: g(x) = (x-2)^3
3. Determine the quadratic function f whose vertex is (3, -2) and passes through (2, 1)
4. Graph the line containing the point P and having slope m: P = (2, -7); m = 0
5. Graph the function and state the vertex, the axis of symmetry, the intercepts, if any: f(x) = x^2-6x+5
What is the vertex?
What is the axis of symmetry?
What are the intercepts, if any?

Solution Preview

1.

This parabola has a vertex at

We see that as the function approaches , so the vertex point is a maxima (the parabola opens down).
The parabola intersects the x-axis when

Which gives:

It intersects the y-axis when x=0 and this gives:

To summarize:
The parabola has a vertex which is a maxima at so its symmetry axis is x=1
It intersects the x-axis at and
It intersects the y-axis at ...

Solution Summary

The solution assists with completing the square, quadratic functions, axis of symmetry and intercepts. The axis of symmetry and intercepts are analyzed.

... equation of the axis of symmetry for the graph of the ... object after t seconds is given by the function h = - 16 ... X 9 = 0 2 5) solve by completing the square...

...Quadratic Functions, Solving, Factoring anf Applications are investigated ... b) Graph the function using the equation in part a ... The vertex of the first graph is (0,0 ...

... f) What is the image set of the function f? (you ... Please see the attached file for the complete solution. ... a) From the graph of , we can obtain by the following ...

... Please see the attached file for the complete solution. ... The graph of the data in the table ... 4 -5 The path of a falling object is given by the function s = −16t ...

... A Complete, Neat and Step-by-step Solution is provided in the attached file ...Graph: The path of a falling object is given by the function s = -16t 2 + v0 t + s 0 ...

... equation has no real roots and so the graph of y ... Rewrite the quadratic function on the left hand side in the form a (x Â± b)2 Â± c by completing the square...

... of a falling object is given by the function s = −16t ... seconds Show your work here: By completing the squares... 4 Thus, after 1.25 seconds, the graph reaches its ...

... Please see the attached file for the complete solution ... list to learn more about how to graph in MS ... path of a falling object is given by the function s = −16t ...

... 6. Graph the equations by completing the tables and plotting ... b) Does this function have a maximum or a minimum? ... you obtain your answer by looking at the graph: ...