(a) Copy and complete the table of values for the... | WAEC SSCE - General Mathematics - 2019

Question 1 Report

(a) Copy and complete the table of values for the relation \(y = 4x^2 - 8x - 21\), for \(-2.0 \leq x \leq 4.0\)

x	-2.0	-1.5	-1.0	0.5	0.0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
y	11		-9		-21	-24			-21		-9	0

(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation \(y = 4x^2 - 8x - 21\)

(ii) Use the graph to find the solution set of

(\(\alpha\)) \(4x^2 - 8x = 3\);

(\(\beta\)) \(4x^2 - 7x - 21 = 0\)

Answer

(a) For the missing entry between rm x=-1.0 rm and rm x=0.0 rm , the intended value is rm x=-0.5 rm . The completed table is:

x	-2.0	-1.5	-1.0	-0.5	0.0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
y	11	0	-9	-16	-21	-24	-25	-24	-21	-16	-9	0	11

For example, when rm x=-1.5 rm ,

\[y=4(-1.5)^2-8(-1.5)-21=9+12-21=0.\]

(b)(i) The graph of rm y=4x^2-8x-21 rm is shown below. The plotted curve uses the stated scales: 2 cm represents 1 unit on the rm x rm -axis and 2 cm represents 5 units on the rm y rm -axis.

(b)(ii)( rm rm )

\[4x^2-8x=3\]

Since rm y=4x^2-8x-21 rm , this gives

\[y=3-21=-18.\]

From the intersections of the curve with the line rm y=-18 rm ,

\[\boxed{x\approx -0.35\quad\text{or}\quad x\approx2.3}.\]

(b)(ii)( rm rm )

\[4x^2-7x-21=0.\]

Writing this in terms of the plotted curve,

\[4x^2-8x-21=-x,\]

so draw the line rm y=-x rm . From its intersections with the curve,

\[\boxed{x\approx-1.6\quad\text{or}\quad x\approx3.3}.\]

Read lesson note on Quadratic Equations (WAEC)

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

Answer Details

(a) For the missing entry between rm x=-1.0 rm and rm x=0.0 rm , the intended value is rm x=-0.5 rm . The completed table is:

x	-2.0	-1.5	-1.0	-0.5	0.0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
y	11	0	-9	-16	-21	-24	-25	-24	-21	-16	-9	0	11

For example, when rm x=-1.5 rm ,

\[y=4(-1.5)^2-8(-1.5)-21=9+12-21=0.\]

(b)(i) The graph of rm y=4x^2-8x-21 rm is shown below. The plotted curve uses the stated scales: 2 cm represents 1 unit on the rm x rm -axis and 2 cm represents 5 units on the rm y rm -axis.

(b)(ii)( rm rm )

\[4x^2-8x=3\]

Since rm y=4x^2-8x-21 rm , this gives

\[y=3-21=-18.\]

From the intersections of the curve with the line rm y=-18 rm ,

\[\boxed{x\approx -0.35\quad\text{or}\quad x\approx2.3}.\]

(b)(ii)( rm rm )

\[4x^2-7x-21=0.\]

Writing this in terms of the plotted curve,

\[4x^2-8x-21=-x,\]

so draw the line rm y=-x rm . From its intersections with the curve,

\[\boxed{x\approx-1.6\quad\text{or}\quad x\approx3.3}.\]