Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically
Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically
IP 2
8 marks
The variables \(x\) and \(y\) are connected by the equation \(y = -x^2 + 2x + 3\). Some corresponding values of \(x\) and \(y\) are given in the table below.
| \(x\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|---|---|---|
| \(y\) | \(-5\) | \(a\) | \(3\) | \(4\) | \(3\) | \(0\) | \(-5\) |
Calculate the value of \(a\).
[1]On the grid provided on the next page, plot the points given in the table and join them with a smooth curve.
[3]Use your graph to find the values of \(x\) when \(y = 1.4\).
[2]Write down the equation of the line of symmetry of the graph.
[1]Using your graph, explain why \(y = -x^2 + 2x + 3\) does not have any solution when \(y = 5\).
[1]
Solution:
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Answer:(a) \(a=0\)
(b) Plot:\((-2,-5),\ (-1,0),\ (0,3),\ (1,4),\ (2,3),\ (3,0),\ (4,-5)\). Join the points with a smooth curve.
(c)\(x\approx -0.6\text{ or}\hspace{0.5em} x\approx2.6\)(d) \(x=1\) (e) No real solution when \(y=5\).
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