Quadratics In Vertex Form Worksheet (Page 3 of 4) in pdf

Quadratics In Vertex Form Worksheet Page 3

Get the Gizmo ready:

Activity B:

 Set a to 1.0, h to 1.0, and k to –4.0.

 Turn on Show vertex and intercept(s).

The intercepts

 Turn off Show axis of symmetry.

1. The function graphed in the Gizmo should be y = (x – 1)

– 4.

A. The y-intercept of the graph is the value of y when x

is zero. Write an equation for the y-intercept of this

graph. Then simplify the equation in the space to the

right. Check your answer by comparing it to the

y-intercept given in the Gizmo.

B. Now simplify the right side of the equation y = a(0 – h)

+ k. What is the general

equation of the y-intercept? y =

Experiment with a variety

of quadratic functions to check that this equation always works.

2. Graph the function y = (x – 1)

– 4 again.

A. The x-intercepts of the graph are the values of x

when y is zero. Substitute zero for y in y = (x – 1)

– 4

and solve for x. Show your work in the space to the

right. Check your answer by comparing it to the

x-intercepts given in the Gizmo.

B. Turn on Show axis of symmetry to see the axis of symmetry. How do the locations

of the x-intercepts of this graph relate to the axis of symmetry?

Vary the value of k to check that this relationship always exists.

C. Solve the equation 0 = a(x – h)

+ k for x to

find the general equation of the x-intercepts.

Show your work in the space to the right.

(Remember that square roots can be

positive or negative.)

D. How does the general equation prove that the x-intercepts are equidistant from the

axis of symmetry? (Hint: Recall that the equation for the axis of symmetry is x = h).

(Activity B continued on next page)

Quadratics In Vertex Form Worksheet Page 3