Does the sign of the

x2-term affect the

parabola's width?

No. The sign o f th e

x2-term affects only

whether the parabola

opens upward or

downward.

jQ b lS iL M m H n B
What values should
yo u choose f o r x?
Use th e same values
of x for graphing both
fu n c tio n s so th a t you
can see the rela tio n sh ip
between corresponding
y-coordinates.

The coefficient of the x2-term in a quadratic function affects the width of a parabola

as well as the direction in which it opens. When j m\ < \n\, the graph of y = mx 2 is

wider than the graph of y = nx2.

Pr o b l em 3 Com p aring W idt hs of Par ab o l as

Use the graphs below. What is the order, from widest to narrowest, of the graphs of

the quadratic functions fix) = — 4 x 2, / ( x ) = | x 2, and fix ) = x 21

fix) = -4x 2 fix) = |x (^2) fix) = X2

n

Of the three graphs, /(x) = \x2 is the widest and /(x) = -4 x 2 is the narrowest. So, the

order from widest to narrowest is fix) = 4 x , / ( x ) = x , and fix) = -4 x 2.

Go t It? 3. What is the order, from widest to narrowest, of the graphs of the functions

fix) = -x 2, fix) = 3x2, and fix) = ~ h x 2l

The y-axis is the axis of symmetry for graphs of functions of the form y= ax2 + c. The

value of c translates the graph up or down.

Pr o b l em 4 Gr ap h i n g y = a x 2 + c

Multiple Choice How is the graph of y = 2x2 + 3 different from the graph of y = 2x2?

CAf It is shifted 3 units up.

C3D It is shifted 3 units down.

X y = 2x2 y = 2x2 + 3

-2 811

-1^25

0 0 3

1 2 5

2 8 11

C O It is shifted 3 units to the right.

C O It is shifted 3 units to the left.

y

rU

1

X

—— 0

The graph of y = 2x 2 + 3 has the same shape as the graph of y = 2x 2 but is shifted up

3 units. The correct answer is A.

Go t I t? 4. Graph y = x 2 and y = x 2 — 3. How are the graphs related?

548 Ch ap t er 9 Quadratic Functions and Equations