Question: Match the function with its graph, using the discriminant y = 2x2 - 4x + 2.



A ) Graph-2
B ) Graph-3
C ) Graph-1
D ) none of the above

Steps to derive

1 y = 2x2 - 4x + 2

2 2x2 - 4x + 2 = 0
 [Write the equation in standard form.]

3 Compare the equation with the standard form ax2 + bx + c = 0 to get the values of a, b and c.

4 b2 - 4ac = (- 4)2 - 4(2)(2)
 [Substitute the values.]

 [Simplify.]
5 = 16 - 16 = 0

6 Since the discriminant is zero, the quadratic equation has only one solution.

7 The x-intercepts occur when y = 0. The graph, y = 2x2 - 4x + 2 touches the x-axis at a point.

8 Among the given graphs, graph-1 touches the x-axis at (1, 0). So, the given function matches graph-1.



Hence the right answer is Option C

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