The table is for the relation \(y = px^{2} - 5x + q\). x -3 -2 -1 0 1 2 3 4 5 y 21 6 -12 0 13 (a)(i) Use the table to find the values of p and q. (ii) Copy ...
Question 1 Report
The table is for the relation \(y = px^{2} - 5x + q\).
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y | 21 | 6 | -12 | 0 | 13 |
(a)(i) Use the table to find the values of p and q.
(ii) Copy and complete the table.
(b) 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 \(-3 \leq x \leq 5\).
(c) Use the graph to find :
(i) y when x = 1.8 ; (ii) x when y = -8.
Answer Details
(a)(i) Given that \(y=px^2-5x+q\).
When \(x=0\), \(y=-12\):
\[q=-12.\]
When \(x=4\), \(y=0\):
\[0=16p-5(4)-12\]
\[0=16p-32\]
\[p=2.\]
Therefore,
\[\boxed{y=2x^2-5x-12}.\]
(a)(ii) The completed table is:
| \(x\) | \(-3\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
|---|---|---|---|---|---|---|---|---|---|
| \(y\) | \(21\) | \(6\) | \(-5\) | \(-12\) | \(-15\) | \(-14\) | \(-9\) | \(0\) | \(13\) |
(b) The graph of \(y=2x^2-5x-12\), plotted using the stated scales, is shown below.
(c)
(i) From the graph, when \(x=1.8\),
\[\boxed{y\approx -14.5}.\]
(ii) Drawing the horizontal line \(y=-8\) and reading the two points of intersection with the curve gives
\[\boxed{x\approx -0.65\text{ or }x\approx 3.15}.\]
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