The quadratic y = a(x + b)^2 + c (with a > 0 ) has its minimum value -4 at x = -3. What are b and c?

Worked solution for TMUA-P1-MM8-007 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM8-007 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-007 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-007?

No — calculators are banned in the TMUA. TMUA-P1-MM8-007 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM8-007?

TMUA-P1-MM8-007 is Paper P1 · Graphs of functions (specification code MM8), level 2. Drill more of the same topic from this page.

TMUA-P1-MM8-007 — Paper P1 · Graphs of functions · Level 2

P1MM8Level 2~180s target

Spec: MM8 · No calculator · ~180s

The quadratic

y = a(x + b)^2 + c

(with

a > 0

) has its minimum value

-4

x = -3

. What are

b

and

c

Options

$b = -3$ , $c = -4$
$b = -3$ , $c = 4$
$b = 3$ , $c = 4$
$b = 3$ , $c = -4$
$b = 4$ , $c = -3$

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: vertex-parameters, sign-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The minimum of

a(x+b)^2 + c

sits at

x = -b

, so

-b = -3

gives

b = 3

, and the minimum value

c = -4

. Trap:

b = -3

copies the sign of the vertex directly — plausible if you forget the minus already in

(x + b)

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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: sign-trap

P1MM4Level 2

TMUA-P1-MM4-005

A triangle has sides of length 5 and 7 with included angle 60^°. What is the length of the third side?

Trigonometry

Open TMUA-P1-MM4-005 →

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-MM8-007 — Paper P1 · Graphs of functions · Level 2

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-007 — Paper P1 · Graphs of functions · Level 2

Options

Keep practising

Master Graphs of functions