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Question
Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x2 + 6x + 9
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Solution
y = x2 + 6x + 9
y = x2 + 6x + 9 ......(3)
Compare this equation with the equation
ax2 + bx + c = 0
We have a = 1, b = 6, c = 9
b2 – 4ac = 62 – 4 × 1 × 9
= 36 – 36
= 0
Since the discriminant is zero the quadratic equation has real and equal roots and therefore the graph touches the x-axis at one point.
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