Arcing ArcherArrowfolk · inequalities

Arrows that fly in arcs: quadratic inequalities.

Quadratic Inequalities

Quadratic inequalities. In MathBound, the free Algebra I adventure game, Arcing Archer asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

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

What you will practice

Quadratic Inequalities. Read the solution of f(x) > 0 or f(x) < 0 from a graphed parabola.
Nonlinear Inequalities in Two Variables. Decide whether a point satisfies y > x^2 + c or y <= |x - h| + k.

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

Which

point

is

NOT

a

solution

of

y \leq (x + 3)^{2} - 2 ?

Show the worked steps

$For$ $(1, 17) :$ $the$ $right$ $side$ $is$ $14,$ $and$ $17 \leq 14$ $is$ $false.$
$So$ $(1, 17)$ $is$ $not$ $a$ $solution;$ $the$ $others$ $are.$

Answer: $(1, 17)$

Solve:

(x - 6) (x - 8) < 0

Show the worked steps

$Boundary$ $points:$ $(x - 6) (x - 8) = 0$ $when$ $x = 6$ $or$ $x = 8 .$
$Test$ $x = 7$ $between$ $them:$ $the$ $expression$ $is$ $negative$ $there,$ $and$ $positive$ $outside.$
$So$ $(x - 6) (x - 8) < 0$ $for$ $6 < x < 8 .$

Answer: $6 < x < 8$

Which

point

is

a

solution

of

y \leq ∣ x + 1 ∣ + 4 ?

Show the worked steps

$Put$ $each$ $point$ $in:$ $a$ $solution$ $makes$ $y \leq ∣ x + 1 ∣ + 4$ $true.$
$For$ $(3, 5) : 5 \leq 8$ $is$ $true.$

Answer: $(3, 5)$

Textbook	Lessons
Carnegie Learning Algebra I	M5 3.1
CPM Core Connections Algebra	9.3.2, 10.3.3
Math Nation Algebra 1 (Florida B.E.S.T.)	8.2