Fountain FionaArcfolk · quadratics

Her fountain arcs in every form: vertex, intercept and standard form.

Forms of Quadratic Functions

Vertex, intercept and standard form. In MathBound, the free Algebra I adventure game, Fountain Fiona 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

Vertex Form. Give the vertex of y = a(x - h)^2 + k.
Intercept Form. Give the x-intercepts of y = a(x - p)(x - q).
Transformations of y = x^2. Describe y = x^2 + k as a vertical shift.

Worked examples

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

Example 1 · Vertex Form

What

is

the

vertex

of

y = (x + 1)^{2} - 3 ?

$(- 1, - 3)$
$(- 1, 3)$
$(1, - 3)$
$(1, 3)$

Show the worked steps

$y =$ $a (x - h)^{2} + k$ $has$ $its$ $vertex$ $at$ $(h, k) .$
$Here$ $the$ $vertex$ $is$ $(- 1, - 3) .$

Answer: $(- 1, - 3)$

Example 2 · Intercept Form

Which

equation

of

the

parabola

y = 2 x^{2} - 24 x + 64

shows

its

vertex

most

directly?

$y = 2 (x + 6)^{2} - 8$
$y = 2 (x - 8) (x - 4)$
$y = 2 (x - 6)^{2} - 8$
$y = 2 (x - 6)^{2} + 8$

Show the worked steps

$Vertex$ $form$ $y =$ $a (x - h)^{2} + k$ $shows$ $the$ $vertex$ $(6, - 8) .$
$So$ $y = 2 (x - 6)^{2} - 8 .$

Answer: $y = 2 (x - 6)^{2} - 8$

Example 3 · Transformations of y = x^2

The

point

(1, 1)

is

on

the

graph

of

y = x^{2} .

Which

point

is

on

the

graph

of

y = x^{2} - 1 ?

$(2, 1)$
$(1, 2)$
$(1, 0)$
$(0, 1)$

Show the worked steps

$A$ $vertical$ $shift$ $of$ $- 1$ $moves$ $every$ $point$ $down$ $by$ $1 .$
$(1, 1)$ $moves$ $to$ $(1, 0) .$

Answer: $(1, 0)$

Where it is in your textbook

Textbook	Lessons
Standard course	9.1, 9.3, 9.4
Big Ideas Math Algebra 1	8.1, 8.2, 8.4, 8.5, 9.2, 9.4
Big Ideas Math Algebra 1 (2022)	8.1, 8.2, 8.4, 8.5, 9.2, 9.4
Carnegie Learning Algebra I	M5 1.2, M5 1.3, M5 2.3
CPM Core Connections Algebra	8.2.2, 8.2.4, 8.2.5, 11.1.1, 11.3.4
CPS Skyline Algebra	7.1-7.2, 7.9, 7.10, 8.7
enVision Algebra 1	8-1, 8-2, 9-2, 10-4, 10-5
enVision Algebra 1 (2024)	8-1, 8-2, 9-2, 10-4, 10-5
Eureka Math Algebra I (EngageNY)	4.8-4.10, 4.16-4.17, 4.19-4.21, 4.22, 5.4
Glencoe Algebra 1	9-3
HMH Into Algebra 1	19.1, 19.2, 19.3
Holt McDougal Larson Algebra 1	9.1, 9.3
Illustrative Mathematics Algebra 1	6.10-6.11, 6.15-6.17, 7.22-7.23
Illustrative Mathematics Algebra 1 (v.360)	7.10-7.11, 7.15-7.17, 8.22-8.23
Math Nation Algebra 1 (Florida B.E.S.T.)	8.3, 8.4, 8.7, 8.9, 9.1, 9.2, 9.3, 9.4, 13.5, 13.6, 13.7, 13.H1
MVP Mathematics I (Integrated Math 1)	3.6
Open Up NC Math 1 (MVP)	6.4, 7.1, 7.6, 7.8
Pearson Algebra 1 Common Core	9-1
Reveal Algebra 1	11-2, 11-4, 11-5
SpringBoard Algebra 1	30, 31

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