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8.04 The quadratic formula and the discriminant

Adaptive
Worksheet

Interactive practice questions

The standard form of a quadratic equation is $ax^2+bx+c=0$ax2+bx+c=0.

Identify the values of $a$a, $b$b and $c$c in the quadratic equation $x^2+7x+10=0$x2+7x+10=0 with $a>0$a>0.

$a$a $=$= $\editable{}$
$b$b $=$= $\editable{}$
$c$c $=$= $\editable{}$
Easy
< 1min

The standard form of a quadratic equation is $ax^2+bx+c=0$ax2+bx+c=0.

Identify the values of $a$a, $b$b and $c$c in the quadratic equation $x^2-3x-4=0$x23x4=0 with $a>0$a>0.

Easy
< 1min

The standard form of a quadratic equation is $ax^2+bx+c=0$ax2+bx+c=0.

Identify the values of $a$a, $b$b and $c$c in the quadratic equation $2x^2+9x=0$2x2+9x=0 with $a>0$a>0.

Easy
< 1min

Solve $-6+7x+5x^2=0$6+7x+5x2=0 for $x$x by using the quadratic formula or otherwise.

Write each solution on the same line, separated by a comma.

Easy
3min
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Outcomes

A1.N.Q.A.1

Use units as a way to understand real-world problems.*

A1.N.Q.A.1.D

Choose an appropriate level of accuracy when reporting quantities.*

A1.A.CED.A.1

Create equations and inequalities in one variable and use them to solve problems in a real-world context.*

A1.A.REI.A.1

Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

A1.A.REI.B.3

Solve quadratic equations and inequalities in one variable.

A1.A.REI.B.3.A

Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has solutions that are not real numbers.

A1.MP1

Make sense of problems and persevere in solving them.

A1.MP3

Construct viable arguments and critique the reasoning of others.

A1.MP6

Attend to precision.

A1.MP7

Look for and make use of structure.

A1.MP8

Look for and express regularity in repeated reasoning.

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