Why isn't the answer to TMUA-P1-MM8-019 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-019 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-019?

No — calculators are banned in the TMUA. TMUA-P1-MM8-019 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM8-019?

TMUA-P1-MM8-019 is Paper P1 · Graphs of functions (specification code MM8), level 2. Drill more of the same topic from this page.

TMUA-P1-MM8-019 — Paper P1 · Graphs of functions · Level 2

P1MM8Level 2~150s target

Spec: MM8 · No calculator · ~150s

What is the vertex of

y = x^2 - 6x + 8

Options

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

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: quadratic-vertex, completing-the-square. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Complete the square:

(x-3)^2 - 9 + 8 = (x-3)^2 - 1

, so the vertex is

(3, -1)

and the correct is A. Trap:

(-3, 1)

flips both signs.

Keep practising

Same topic · same level
P1MM8Level 2
TMUA-P1-MM8-004
How is the graph of y = f(x) + 2 obtained from the graph of y = f(x)?
Graphs of functions
Open TMUA-P1-MM8-004 →
Same trap: completing-the-square
P1MM1Level 1
TMUA-P1-MM1-005
Write x^2 + 6x + 5 in the form (x + a)^2 + b. What is the value of b?
Algebra and functions
Open TMUA-P1-MM1-005 →
Step up a level
P1MM8Level 3
TMUA-P1-MM8-009
Which statement correctly describes the stationary points of y = x^3 - 3x^2?
Graphs of functions
Open TMUA-P1-MM8-009 →

Browse more

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Keep practising

Same topic · same level

P1MM8Level 2

TMUA-P1-MM8-004

How is the graph of y = f(x) + 2 obtained from the graph of y = f(x)?

Graphs of functions

Open TMUA-P1-MM8-004 →

Same trap: completing-the-square

P1MM1Level 1

TMUA-P1-MM1-005

Write x^2 + 6x + 5 in the form (x + a)^2 + b. What is the value of b?

Algebra and functions

Open TMUA-P1-MM1-005 →

Step up a level

P1MM8Level 3

TMUA-P1-MM8-009

Which statement correctly describes the stationary points of y = x^3 - 3x^2?

Graphs of functions

Open TMUA-P1-MM8-009 →

TMUA-P1-MM8-019 — Paper P1 · Graphs of functions · Level 2

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-019 — Paper P1 · Graphs of functions · Level 2

Options

Keep practising

Master Graphs of functions