11. Quadratic Equations

11.01 Solving using graphs and tables

11.02 Solving by factoring

11.03 Solving using square roots

11.04 Solve using the quadratic formula

11.05 Solving using appropriate methods

11.06 Linear-quadratic systems

11.07 Quadratic inequalities

United States of America

Grades 9-12

11.03 Solving using square roots

Adaptive

Worksheet

Interactive practice questions

Solve the following equation for $x$x:

$x^2=81$x2=81

Write all solutions on the same line, separated by commas.

Medium

< 1min

Solve for $x$x:

$x^2-25=0$x2−25=0

Medium

< 1min

Solve the following equation for $x$x:

$x^2=10$x2=10

Medium

< 1min

Solve for $x$x:

$x^2-5=31$x2−5=31

Medium

< 1min

Outcomes

A.CED.A.1

Create equations and inequalities in one variable and use them to solve problems.

A.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.A.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.REI.B.4

Solve quadratic equations in one variable.

A.REI.B.4.A

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

A.REI.B.4.B

Solve quadratic equations by inspection (e.g. For x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

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