For the given graph of y=ax2+bx+c as shown, select the correct statements.
A
y<0∀x∈(α,β)
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B
y>0∀x∈(−∞,α)∪(β,∞)
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C
D>0
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D
a>0
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Solution
The correct option is Da>0 Given the graph of y=ax2+bx+c as shown:
Now, from the graph, we can observe the graph is an upward opening parabola ⇒a>0
Also, the graph cuts the x− axis at two distinct points. ⇒D>0
Also, as observed from the graph: y>0∀x∈(−∞,α)∪(β,∞)&y<0∀x∈(α,β).