Algebra 1 Common Core Student Edition, Grade 8-9

Solving Q uadratic

Equations

Co m m o n Co r e St at e St a n d a r d s

A-REI.B.4b Solve quadratic equations by inspection

(e.g., f o r x 2 = 49), taking square ro o ts... Also

A-APR.B.3, A-CED.A.1, A-CED.A.4

MP 1, MP 2, MP 3, MP 4, MP 7

Objective To solve quadratic equations by graphing and using square roots

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How do you know?

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( MATHEMATICAL

PRACTICES -jpg situation in the Solve It can be modeled by a quadratic equation.

Lesso n i

Vocabulary

quadratic

equation

• stan d ard form
  of a quadratic
  equation


• root o f an
  equation


• zero o f a fu n ction

Key Concept Standard Form of a Quadratic Equation

A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0,

where a ¥= 0. This form is called the standard form of a quadratic equation.

Esse n t i a l U n d e r st a n d i n g Quadratic equations can be solved by a variety of

methods, including graphing and finding square roots.

One way to solve a quadratic equation ax2 + bx + c = 0 is to graph the related

quadratic function y = a x 2 + bx + c. The solutions of the equation are the

x-intercepts of the related function.

1 y

X

To solve

y2 _ a — n

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V
A quadratic equation can have two, one, or no real-number solutions. In a future course
you will learn about solutions of quadratic equations that are not real numbers. In this
course, solutions refers to real-number solutions.
The solutions of a quadratic equation and the x-intercepts of the graph of the related
function are often called roots o f th e e q u a tio n or zeros o f th e function.
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PowerAlgebra.com | Lesso n 9- 3 So l v i n g Q u a d r a t i c Eq u a t i o n s 561