(a) Copy and complete the table for \(y = 3x^{2} -... | WAEC SSCE - General Mathematics - 1996 (Essay)

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(a) Copy and complete the table for \(y = 3x^{2} - 5x - 7\)

x	-3	-2	-1	0	1	2	3	4
\(y = 3x^{2} - 5x - 7\)	35			-7	-9		5

(b) Using a scale of 2cm = 1 unit along the x- axis and 2cm = 5 units along the y- axis, draw the graph of \(y = 3x^{2} - 5x - 7\).

(d) From your graph, find the : (i) range of values of x for which \(3x^{2} - 5x - 7 < 0\) ; (ii) roots of the equation \(3x^{2} - 2x - 5 = 0\).

Answer

(a) For \(y=3x^{2}-5x-7\), the completed table is:

\(x\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)
\(y=3x^2-5x-7\)	35	15	1	−7	−9	−5	5	21

For example, when \(x=-2\),

\[ y=3(-2)^2-5(-2)-7=12+10-7=15. \]

(b) and (c) The required graphs, drawn on the same axes, are shown below. The curve is \(y=3x^2-5x-7\), and the straight line is \(y=-3x-2\).

(d)(i) \(3x^2-5x-7<0\) where the parabola lies below the \(x\)-axis. Reading the intercepts from the graph gives approximately \(-0.9\) and \(2.6\). Hence,

\[ -0.9<x<2.6. \]

(d)(ii) The roots of \(3x^2-2x-5=0\) are the \(x\)-coordinates of the points where the line and curve intersect:

\[ 3x^2-5x-7=-3x-2 \] \[ 3x^2-2x-5=0. \] From the graph,

\[ x=-1.0\quad\text{or}\quad x\approx1.7. \]

Indeed, \(3x^2-2x-5=(3x-5)(x+1)\), so the exact roots are \(x=-1\) and \(x=\frac53\).

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Answer Details

(a) For \(y=3x^{2}-5x-7\), the completed table is:

\(x\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)
\(y=3x^2-5x-7\)	35	15	1	−7	−9	−5	5	21

For example, when \(x=-2\),

\[ y=3(-2)^2-5(-2)-7=12+10-7=15. \]

(b) and (c) The required graphs, drawn on the same axes, are shown below. The curve is \(y=3x^2-5x-7\), and the straight line is \(y=-3x-2\).

(d)(i) \(3x^2-5x-7<0\) where the parabola lies below the \(x\)-axis. Reading the intercepts from the graph gives approximately \(-0.9\) and \(2.6\). Hence,

\[ -0.9<x<2.6. \]

(d)(ii) The roots of \(3x^2-2x-5=0\) are the \(x\)-coordinates of the points where the line and curve intersect:

\[ 3x^2-5x-7=-3x-2 \] \[ 3x^2-2x-5=0. \] From the graph,

\[ x=-1.0\quad\text{or}\quad x\approx1.7. \]

Indeed, \(3x^2-2x-5=(3x-5)(x+1)\), so the exact roots are \(x=-1\) and \(x=\frac53\).

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Inequalities (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Read lesson note on Graphs Of Linear And Quadratic Functions (WAEC)

Algebraic Expressions

Inequalities

Quadratic Equations

Graphs Of Linear And Quadratic Functions

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(a) Copy and complete the table for \(y = 3x^{2} - 5x - 7\) x -3 -2 -1 0 1 2 3 4 \(y = 3x^{2} - 5x - 7\) 35 -7 -9 5 (b) Using a scale of 2cm = 1 unit along ...

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(a) Copy and complete the table for \(y = 3x^{2} - 5x - 7\) x -3 -2 -1 0 1 2 3 4 \(y = 3x^{2} - 5x - 7\) 35 -7 -9 5 (b) Using a scale of 2cm = 1 unit along ...

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