4. Quadratics

4.01 Key features of quadratic functions

4.02 Solving quadratic equations by factoring

4.03 Solving quadratic equations using square roots

Investigation: Deriving the quadratic formula

4.04 The discriminant and the quadratic formula

4.05 Graphing quadratic functions

4.06 Transformations of quadratics

4.07 Quadratics in factored form

4.08 Quadratics in vertex form

4.09 Quadratic functions and technology

4.10 Applications of quadratic functions

4.11 Comparing exponential and quadratic functions

4.12 Systems of linear and quadratic equations

United States of America CA

Math 2

4.04 The discriminant and the quadratic formula

Interactive practice questions

Below is the result after using the quadratic formula to solve an equation.

$x=\frac{10\pm\sqrt{-1}}{8}$x=10±√−18

The equation has $two real solutions$ .

A

The equation has $one real solution$ .

B

The equation has $no real solution$ .

C

Easy

< 1min

Consider the equation $x^2+6x+9=0$x2+6x+9=0.

Easy

1min

Consider the equation $4x^2-6x+7=0$4x2−6x+7=0.

Easy

1min

Which of the following equations does not have any real solutions?

Easy

1min

Outcomes

N-CN.7

Solve quadratic equations with real coefficients that have complex solutions.

A-CED.1

Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions

A-REI.4

Solve quadratic equations in one variable. [Quadratics with real coefficients]

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