Algebra Period 3 (Tuesday)

Review of how to graph a quadratic

Find the vertex ( x = -b/2a, then plug in to the equation to find the y coordinate)

Find the axis (line) of symmetry. Just use the x value of the vertex that is
x = -b/2a

Draw the line of symmetry using a dotted or dashed line

Find 2 more points in an x y table (go either left or right of the vertex and use 2 points close to the line of symmetry for the x, then plug into the equation to find the y values)

Find the 2 shadow (mirror) points by counting over from the axis at the exact same y value

Draw a U (not a V) through the points. Extend it past and put arrows at the end
Remember to label the x and y axes and put arrows on the axes.

Function vs. Relations: Functions are special relations where there is a unique x for each y
Therefore, there will never be 2 x’s that will repeat and if you use a vertical line on the graph, it will only hit one point on the graph.

Domain vs. Range: the domain for any quadratic function is ALL REAL NUMBERS
The range depends on where the vertex is and whether the quadratic is a smile or a frown.
Generally, it will be of the form:

y such that y is either greater than or equal to (≥ ) or less than or equal to (≤) the y value of the vertex. {y l y≥ n} or {y l y ≤ n}

f(x) is just a different way of saying y. What is better about it? Without seeing the work before the solution, you can actually tell the x value as well as the y value in the solution.

For example, if the solution is f(-3) = 12 you know that the point is (-3, 12)
Compare that to the solution y = 12. For that solution, you would not know the x value unless you look back in the problem.