Drawing & Using Graphs

Topic

Higher June 2025 Paper 2 Q25

EdexcelCurrent spec6 marksCompleting the Square Drawing & Using Graphs

(a) Write \(28 + 24x - 6x^2\) in the form \(a - b(x - c)^2\) where \(a\), \(b\) and \(c\) are integers. (3)

(b) On the axes below, sketch the graph of \(y = 28 + 24x - 6x^2\)
Show clearly the coordinates of the turning point and the coordinates of the point of intersection of the graph with the \(y\)-axis. (3)

Mark scheme (a)

Scheme	Marks
\(\pm 6\left(x \pm \dfrac{4}{2}\right)^2\ldots\ldots\) or \(\pm 6(x \pm 2)^2\ldots\ldots\) or \(\pm 6\left[(x \pm 2)^2\ldots\ldots\right]\) or \(\pm 6\left[\left(x \pm \dfrac{4}{2}\right)^2\ldots\ldots\right]\) or \(\pm 6\left(x \pm \dfrac{24}{2 \times -6}\right)^2\ldots\)	M1
\(-6\left[\left(x - \dfrac{4}{2}\right)^2 - \left(\dfrac{4}{2}\right)^2\right]\ldots\ldots\) or \(-6\left[(x - 2)^2 - 2^2\right]\ldots\ldots\) or \(-6\left[\left(x - \dfrac{4}{2}\right)^2 - \left(\dfrac{4}{2}\right)^2\ldots\ldots\right]\) or \(-6\left[(x - 2)^2 - 2^2\ldots\ldots\right]\) or \(-6\left(x + \dfrac{24}{2 \times -6}\right)^2 - \dfrac{24^2}{4 \times -6}\ldots\ldots\)	M1
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(52 - 6(x - 2)^2\)	A1
	(3)

Notes

M1: for a start to completing the square

correct substitution into \(a\left(x + \dfrac{b}{2a}\right)^2 + \ldots\) from the formula \(a\left(x + \dfrac{b}{2a}\right)^2 - \dfrac{(b)^2}{4a} + c\)

M1: for correctly completing the square but terms do not need to be simplified and 28 may or may not be present

correct simplification of the first two parts of \(a\left(x + \dfrac{b}{2a}\right)^2 - \dfrac{(b)^2}{4a}(+c)\)

NB: Please refer to ALT mark scheme after (b) for comparison of coefficients method

A1: oe eg \(-6(x - 2)^2 + 52\)

25(a) ALT

Scheme	Marks
\(-bx^2 + 2bcx - bc^2 + a\) and \(b = 6\) or \(b = -6\)	M1
\(2bc = 24\) or \(-bc^2 + a = 28\)	M1
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(52 - 6(x - 2)^2\)	A1

Notes

M1: for multiplying out \(a - b(x - c)^2\) and \(b = 6\) or \(b = -6\)

M1: for equating coefficients

A1: oe eg \(-6(x - 2)^2 + 52\)

Sketch of an n-shaped curve with turning point marked (2, 52) — Mark scheme (b)

Sketch of an n-shaped curve crossing the y-axis at (0, 28) — Mark scheme (b)

Scheme	Marks
‘∩’ or ‘∪’ shaped symmetrical quadratic curve	B1
Answer: Turning point marked as (2, 52)	B1
Answer: Intersection with \(y\)-axis marked as (0, 28) or crossing at 28 marked	B1
	(3)
	(6 marks)

Higher June 2025 Paper 2 Q14

EdexcelCurrent spec2 marksDrawing & Using Graphs

14 Here are five graphs.

Five sketch graphs: A a reciprocal curve, B an n-shaped parabola with maximum on the positive y-axis, C a cubic through the origin, D a u-shaped parabola with minimum on the negative y-axis, E a straight line with negative gradient

(a) Write down the letter of the graph that could have the equation \(y = 5 - x^2\) (1)

(b) Write down the letter of the graph that could have the equation \(y = 2x^3\) (1)

Scheme	Marks
B	B1
	(1)

Scheme	Marks
C	B1
	(1)
	(2 marks)

Higher June 2025 Paper 1 Q10

EdexcelCurrent spec3 marksDrawing & Using Graphs

(a) Complete the table of values for \(y = x^3 + 2x + 3\) (1)

\(x\)	\(-3\)	\(-2\)	\(-1\)	0	1	2	3
\(y\)		\(-9\)	0	3	6		36

(b) On the grid, draw the graph of \(y = x^3 + 2x + 3\) for \(-3 \leqslant x \leqslant 3\) (2)

Grid with x from -3 to 3 and y from -30 to 40

Scheme	Marks
\(-30\), 15	B1
	(1)

Correct curve y = x cubed + 2x + 3 drawn from x = -3 to x = 3, passing through (-3, -30), (0, 3) and (3, 36) — Mark scheme (b)

Scheme	Marks
	M1ft
Correct answer scores full marks (unless from obvious incorrect working) Answer: Correct graph	A1
	(2)
	(3 marks)

Higher November 2024 Paper 1 Q11

EdexcelCurrent spec4 marksDrawing & Using Graphs

(a) Complete the table of values for \(y = 2\left(x + \dfrac{1}{x}\right)\) (2)

\(x\)	0.5	1	2	3	4	5	6
\(y\)			5	6.7			12.3

(b) On the grid, draw the graph of \(y = 2\left(x + \dfrac{1}{x}\right)\) for \(0.5 \leqslant x \leqslant 6\) (2)

Grid with x from 0 to 6 and y from 0 to 13

Mark scheme (b)

Scheme	Marks
Correct graph	M1
Correct answer scores full marks (unless from obvious incorrect working)	A1
	(2)
	(4 marks)

Notes

M1: ft their table dep on B1for at least 6 points plotted correctly (within or on the circles on the overlay)

A1: for correct curve between \(x = 0.5\) and \(x = 6\)

Note: If a fully correct graph is shown, but an incomplete table is shown in (a), then award the marks for (a)

Ignore curve drawn for \(x \lt 0.5\) and \(x \gt 6\)