Quadratic Formula

The quadratic formula and the discriminant. In MathBound, the free Algebra I adventure game, Plus-Minus Pendulum asks these problems, and the only way past is to solve them.

Part of Solving Quadratic Equations: chapter 10 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Identify Coefficients. Identify the coefficients a,b,and c in a quadratic equation written in standard form (ax^2 + bx + c = 0).
Solve with Formula. Solve a quadratic equation using the formula where the discriminant is a perfect square yielding rational solutions.
Standard Form First. Rearrange an equation into standard form before identifying coefficients and applying the formula.
Use the Discriminant. Calculate the discriminant (b^2 - 4ac) to determine if the equation has two,one,or zero real solutions.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Identify Coefficients

In

2 x^{2} + 9 x - 1 = 0,

what

is

the

value

of

c ?

$2$
$9$
$1$
$- 1$

Show the worked steps

$c$ $is$ $the$ $constant$ $term,$ $sign$ $included.$
$So$ $c = - 1 .$

Answer: $- 1$

Example 2 · Solve with Formula

Solve

with

the

quadratic

formula:

x^{2} + 5 x - 6 = 0

$x = 1$ $or$ $x = - 6$
$x = 5$ $or$ $x = - 6$
$x = 1$
$x = - 1$ $or$ $x = 6$

Show the worked steps

$a = 1, b = 5, c = - 6 .$
$The$ $discriminant$ $is$ $5^{2} - 4 \cdot 1 \cdot (- 6) = 49 .$
$x = \frac{- 5 \pm 49}{2},$ $giving$ $1$ $and$ $- 6 .$

Answer: $x = 1$ $or$ $x = - 6$

Example 3 · Standard Form First

Solve:

x (x - 13) = - 42

$x = - 7$ $or$ $x = - 6$
$x = 0$ $or$ $x = 13$
$x = 7$ $or$ $x = 6$
$x = - 42$ $or$ $x = - 29$

Show the worked steps

$Expand$ $and$ $bring$ $- 42$ $across:$ $x^{2} - 13 x + 42 = 0.$
$The$ $discriminant$ $is$ $1,$ $so$ $x = 7$ $or$ $x = 6 .$

Answer: $x = 7$ $or$ $x = 6$

Where it is in your textbook

Textbook	Lessons
Standard course	10.3
Big Ideas Math Algebra 1	9.5
Big Ideas Math Algebra 1 (2022)	9.5
Carnegie Learning Algebra I	M5 2.5
CPM Core Connections Algebra	9.1.2, 9.1.4, 10.2.4, 10.2.5, 10.3.2
CPS Skyline Algebra	7.11, 7.12-7.13
enVision Algebra 1	9-6, 9-7
enVision Algebra 1 (2024)	9-5, 9-6
Eureka Math Algebra I (EngageNY)	4.14-4.15
Glencoe Algebra 1	9-5
HMH Into Algebra 1	18.3, 18.4
Holt McDougal Larson Algebra 1	9.6
Illustrative Mathematics Algebra 1	7.16-7.19, 7.20-7.21
Illustrative Mathematics Algebra 1 (v.360)	8.16-8.19, 8.20-8.21
Math Nation Algebra 1 (Florida B.E.S.T.)	9.9, 9.10
OpenStax Elementary Algebra 2e	10.3
Pearson Algebra 1 Common Core	9-6
Reveal Algebra 1	11-6
SpringBoard Algebra 1	32

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