Algebra 1 Common Core Student Edition, Grade 8-9

Get t i n g Read y!

Make sense of

th e situation.

What is the value

of h(t) when the

flo w erp o t h its th e

ground?

MATHEMATICAL

PRACTICES

As a c a t walks along th e railing of a

balcony, it knocks a flowerpot o ff th e

railing. The function h ( t ) = - 1 6 t 2 + c

gives th e height h of th e flowerpot a f t e r

t seconds when it falls from a height of

c fe e t. How long will it take th e

flowerpot to reach th e ground? Explain

your reasoning.

I\

Vocabulary

quadratic

function

• standard form
  o f a q u a d r a tic
  function


• qu a d ra tic p arent
  fu n c tio n


• parabola


• axis o f sym m etry


• vertex


• m inim um


• m axim um

Recall from Chapter 8 that a polynomial of degree 2, such as -1 6 x 2 + 64, is called

a quadratic polynomial. You can use a quadratic polynomial to define a quadratic

function like the one in the Solve It.

Esse n t i a l U n d e r st a n d i n g A quadratic function is a type of nonlinear function

that models certain situations where the rate of change is not constant. The graph of a

quadratic function is a symmetric curve with a highest or lowest point corresponding to

a maximum or minimum value.

Key Concept Standard Form of a Quadratic Function

A quadratic function is a function that can be written in the form y = ax2 + bx+ c,

where a + 0. This form is called the standard form of a quadratic function.

Examples y = 3x2 y = x 2 + (^9) y = x 2 x 2
Quadratic Graphs
and Their Properties
@ Common Core State Standards
F- I F. C. 7 a Graph linear and quadratic functions and
show intercepts, maxima, and m inim a. Also A-CED.A.2,
F- I F. B. 4 , F- I F. B. 5 , F- BF. B. 3
MP 1, MP 2, MP 3, MP 4, MP 5, MP 6
Objective To graph quadratic functions of the form y = ax2 and y = ax2 + c
The simplest quadratic function f(x) = x2 or y = x2 is the quadratic parent
function.
The graph of a quadratic function is a U-shaped curve called a parabola.
The parabola with equation y = x2 is shown at the right.
You can fold a parabola so that the two sides match exactly. This property is
called symmetry. The fold or line that divides the parabola into two matching
halves is called the axis o f sym metry.
546 Ch ap t er 9 Quadratic Functions and Equations