Arc KiteArcfolk · quadratics

A kite on a parabola-shaped frame: graphing parabolas, the vertex and the axis.

Graphing Parabolas

Graphing parabolas, the vertex and the axis. In MathBound, the free Algebra I adventure game, Arc Kite asks these problems, and the only way past is to solve them.

Part of Quadratic Functions: chapter 9 of the standard course.

Play this battle free

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

What you will practice

Identify Orientation. Determine if a parabola opens upward or downward by checking the sign of the leading coefficient (a).
Find Axis of Symmetry. Calculate the axis of symmetry using the formula x = -b/(2a).
Find Vertex. Calculate the vertex by finding the axis of symmetry and evaluating the equation at that x-value to find y.
Find Intercepts. Find the y-intercept by setting x=0 (which always yields the constant term c).
Graph Parabola. Graph the parabola by plotting the vertex,y-intercept,and utilizing the axis of symmetry to find corresponding points.
Min/Max Applications. Find the minimum or maximum value of a quadratic model by calculating the y-coordinate of the vertex.

Worked examples

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

Example 1 · Identify Orientation

Does

y = - 2 x^{2} - 3 x - 4

have

a

maximum

value

or

a

minimum

value?

$A$ $minimum$ $value$
$Both$ $a$ $maximum$ $and$ $a$ $minimum$
$A$ $maximum$ $value$
$Neither$

Show the worked steps

$a = - 2$ $is$ $negative,$ $so$ $it$ $opens$ $downward .$
$So$ $the$ $vertex$ $is$ $its$ $highest$ $point:$ $a$ $maximum .$

Answer: $A$ $maximum$ $value$

Example 2 · Find Axis of Symmetry

Find

the

axis

of

symmetry

of

y = 2 (x - 6) (x + 2) .

$x = 2$
$x = 4$
$x = - 2$
$x = 6$

Show the worked steps

$The$ $x -intercepts$ $are$ $x = 6$ $and$ $x = - 2 .$
$The$ $axis$ $is$ $halfway$ $between$ $them:$ $x = \frac{6 + ( - 2 )}{2} = 2 .$

Answer: $x = 2$

Example 3 · Find Vertex

Find

the

vertex

of

y = - (x - 3) (x - 9) .

$(6, 9)$
$(- 6, 9)$
$(6, - 9)$
$(6, - 27)$

Show the worked steps

$The$ $roots$ $are$ $3$ $and$ $9,$ $so$ $the$ $vertex$ $is$ $at$ $x = 6,$ $halfway$ $between.$
$At$ $x = 6, y = - (6 - 3) (6 - 9) = 9 .$

Answer: $(6, 9)$

Where it is in your textbook

Textbook	Lessons
Standard course	9.1, 9.2, 9.5, 9.6
Big Ideas Math Algebra 1	8.1, 8.3, 9.2, 9.4
Big Ideas Math Algebra 1 (2022)	8.1, 8.3, 9.2, 9.4
Carnegie Learning Algebra I	M5 1.1, M5 1.2, M5 3.1, M5 3.3
CPM Core Connections Algebra	1.1.3, 8.2.1, 8.2.3, 10.3.3, 11.3.4
CPS Skyline Algebra	6.4, 7.9, 7.10
enVision Algebra 1	8-1, 8-3, 8-4, 9-1
enVision Algebra 1 (2024)	8-1, 8-3, 8-4, 9-1
Eureka Math Algebra I (EngageNY)	4.8-4.10, 4.16-4.17, 4.23-4.24
Glencoe Algebra 1	9-1, 9-2
HMH Into Algebra 1	17.1, 19.2, 19.4
Holt McDougal Larson Algebra 1	9.1, 9.2, 9.3
Illustrative Mathematics Algebra 1	6.5-6.7, 6.10-6.11, 6.12-6.14, 7.22-7.23, 7.24
Illustrative Mathematics Algebra 1 (v.360)	7.5-7.7, 7.10-7.11, 7.12-7.14, 8.22-8.23, 8.24
Math Nation Algebra 1 (Florida B.E.S.T.)	8.1, 8.2, 8.3, 8.4, 8.8, 8.9
Open Up NC Math 1 (MVP)	6.1, 6.4, 7.1
OpenStax Elementary Algebra 2e	10.5
Pearson Algebra 1 Common Core	9-1, 9-2
Reveal Algebra 1	11-1, 11-3
SpringBoard Algebra 1	29, 31

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