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Use the point (0, -12) from the table and substitute x=0 and y=-12 into the relation y = px² − 5x + q.
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2 partsStep-by-step solution
7 stepsPart a(i)· 2 steps
Use the table to find the values of p and q.
Use the point from the table and substitute and into the relation .
Use another point from the table, for example , and substitute , , and into the relation .
The values are and .
The relation is .
Part a(ii)
Copy and complete the table.
Using the relation , we calculate the missing y-values:
For :
For :
For :
For :
The completed table is:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|---|---|---|
| y | 21 | 6 | -5 | -12 | -15 | -14 | -9 | 0 | 13 |
Part b· 5 steps
Using scales of 2cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of the relation for .
Draw the x-axis and y-axis on graph paper.
Mark the x-axis from -3 to 5, with each 2 cm representing 1 unit.
Mark the y-axis to cover the range of y-values (from -15 to 21), with each 2 cm representing 5 units.
Plot the points from the completed table
, , , , , , , , .
Draw a smooth curve connecting all the plotted points.
This curve represents the graph of .
Part c(i)-14.5
y when x = 1.8
Use the graph to find
To find when from the graph, locate on the x-axis. Move vertically from to intersect the curve. From the intersection point, move horizontally to the y-axis to read the corresponding y-value.
Using the equation :
From the graph, would be approximately .
Part c(ii)
x when y = -8
To find when from the graph, locate on the y-axis. Move horizontally from to intersect the curve. From the intersection points, move vertically to the x-axis to read the corresponding x-values.
Using the equation :
Using the quadratic formula :
From the graph, would be approximately .
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