10.1 Graph ax2 + c

A quadratic function is a nonlinear function that can be written in the standard form:

y = ax2 + bx + c where a ≠ 0

Every quadratic function has a U-shaped graph called a parabola.

This section, b = 0 so there is no bx term.

x –2 –1 0 1 2

y

Given: y = 2x2

a. Complete the table of valuesb. Identify its domain and rangec. Compare to the parent function graph of y = x2 d. Graph the function and the parent function

a.

b. D:

R:

c. The function is:

Given: y = - 1/4 x2

a. Complete the table of valuesb. Identify its domain and rangec. Compare to the parent function graph of y = x2 d. Graph the function and the parent function

a.

b. D:

R:

c. The function is:

x –4 –2 0 2 4

y

x –2 –1 0 1 2

y

Given: y = x2 - 2a. Complete the table of valuesb. Identify its domain and rangec. Compare to the parent function graph of y = x2 d. Graph the function and the parent function

a.

b. D:

R:

c. The function is:

x –2 –1 0 1 2

y

Given: y = -2x2 + 4a. Complete the table of valuesb. Identify its domain and rangec. Compare to the parent function graph of y = x2 d. Graph the function and the parent function

a.

b. D:

R:

c. The function is:

Given: y = 1/3x2 - 3a. Complete the table of valuesb. Identify its domain and rangec. Compare to the parent function graph of y = x2 d. Graph the function and the parent function

a.

b. D:

R:

c. The function is:

x –6 –3 0 3 6

           

y          

Example 4b.- MORE PRACTICE

Example 6- Extended Response

Egg Contest For an engineering contest, you have to create a container for an egg so that the container can be dropped from a height of 30 feet without breaking the egg.The height y (in feet) of the dropped container is given by the function y = -16t2 + 30 where t is the time (in seconds since the container is dropped.

a. Graph the function.b. Identify the range of the function in this situation.c. Find the egg’s height at 1 second.d. Use the graph to estimate when the egg is at a height of 10 feet.

e. Use the graph to estimate when the egg is on the ground.

Example 6 x

           

y          

54321

a. Table/Graph

b. R:

c. Height at 1 sec.

d. Approximate time when height is 10 feet.

e. Approximate time when height is 0 feet (ground).