(a) Copy and complete the table of values for \(y... | WAEC SSCE - General Mathematics - 2018

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(a) Copy and complete the table of values for \(y = 2x^{2} + x - 10\) for \(-5 \leq x \leq 4\).

x	-5	-4	-3	-2	-1	0	1	2	3	4
y			5		-9	-10		0

(b) Using scales of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, Draw the graph of \(y = 2x^{2} + x - 10\) for \(-5 \leq x \leq 4\).

(i) \(2x^{2} + x = 10\)

(ii) \(2x^{2} + x - 10 = 2x\)

Answer

(a) For \(y=2x^{2}+x-10\), the completed table is:

\(x\)	\(-5\)	\(-4\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)
\(y\)	\(35\)	\(18\)	\(5\)	\(-4\)	\(-9\)	\(-10\)	\(-7\)	\(0\)	\(11\)	\(26\)

(b) The graph of \(y=2x^{2}+x-10\) is shown below. The straight line \(y=2x\), used in part (c)(ii), is also shown.

(c)(i) \[2x^{2}+x=10\iff 2x^{2}+x-10=0.\] The solutions are the \(x\)-coordinates where the parabola cuts the \(x\)-axis. Hence, \[\boxed{x=-2.5\text{ or }x=2}.\]

(c)(ii) The solutions of \(2x^{2}+x-10=2x\) are the \(x\)-coordinates of the points where the parabola intersects the line \(y=2x\). From the graph, \[\boxed{x=-2\text{ or }x=2.5}.\]

Read lesson note on Quadratic Equations (WAEC)

Answer Details

(a) For \(y=2x^{2}+x-10\), the completed table is:

\(x\)	\(-5\)	\(-4\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)
\(y\)	\(35\)	\(18\)	\(5\)	\(-4\)	\(-9\)	\(-10\)	\(-7\)	\(0\)	\(11\)	\(26\)

(b) The graph of \(y=2x^{2}+x-10\) is shown below. The straight line \(y=2x\), used in part (c)(ii), is also shown.

(c)(i) \[2x^{2}+x=10\iff 2x^{2}+x-10=0.\] The solutions are the \(x\)-coordinates where the parabola cuts the \(x\)-axis. Hence, \[\boxed{x=-2.5\text{ or }x=2}.\]

(c)(ii) The solutions of \(2x^{2}+x-10=2x\) are the \(x\)-coordinates of the points where the parabola intersects the line \(y=2x\). From the graph, \[\boxed{x=-2\text{ or }x=2.5}.\]

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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(a) Copy and complete the table of values for \(y = 2x^{2} + x - 10\) for \(-5 \leq x \leq 4\). x -5 -4 -3 -2 -1 0 1 2 3 4 y 5 -9 -10 0 (b) Using scales of ...

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(a) Copy and complete the table of values for \(y = 2x^{2} + x - 10\) for \(-5 \leq x \leq 4\). x -5 -4 -3 -2 -1 0 1 2 3 4 y 5 -9 -10 0 (b) Using scales of ...

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