Graphing Quadratic Functions Worksheet (Page 2 of 4) in pdf

Graphing Quadratic Functions Worksheet Page 2

Graphing quadratic functions.[rev.4] Class/Section _______Name __________________ Date ________

Skill #6. Finding the y-coordinate of the vertex.

The y-coordinate of the vertex is found by evaluating f(x) at the x-coordinate of the

vertex. In the above example, the y-coordinate of the vertex is f(-b/(2a)) = f(2/3) = -19/3.

(see Skill #1 above).

Skill #7. Finding the roots (also called the x-intercepts).

The roots of a function are the x-values for which the function value (y-value) is zero.

Use factoring; but if the polynomial is not factorable, use the quadratic formula.

The QF (quadratic formula) for the roots of a quadratic function may be stated as follows:

If ax

+bx+c = 0, then

Before evaluating the QF, be sure to write the values of a,b,c (see skill #2).

Note: from this formula, you can see that -b/(2a) is the average of the roots. Further, the

distance between the roots is ± √Δ / a, and the distance along the x axis from either root

√Δ) / (2a) .

to the

line of symmetry is (

Skill #8. Finding the y-intercept.

Find the y-intercept by evaluating the polynomial at x=0.

In our example f(0) = 3(0)

-4(0) -5 = -5. The y-intercept is at the point (0,-5).

Skill #9. Finding the symmetric point.

The symmetric point is at the same height as the y-intercept point. It is symmetric about

the axis of symmetry to the y-intercept; so it is the same distance from the axis of

symmetry as the y-intercept:

(y-intercept) --------- axis ------------ (symmetric point).

So the symmetric point is a distance 2 (-b/2a) = -b/a from the y-axis.

Skill #10. Graphing the quadratic function.

When graphing, do all the above things in order.

Your sketch should show: (a) the roots; (b) the vertex ; (c) the line of symmetry; (d) the

y-intercept; (e) the symmetric point; and perhaps one or two other points.

Skill #11. Solving the quadratic by completing the square. [not discussed here].

Graphing Quadratic Functions Worksheet Page 2