Graphs of Quadratic Equation for different values of D when a<0
For any quadr...
Question
For any quadratic function y=−x2+2x−3,y>0∀
A
x∈R−(0}
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B
x∈ϕ
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C
x∈R
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Solution
The correct option is Bx∈ϕ Given the quadratic equation y=−x2+2x−3
Now, comparing the equation with y=ax2+bx+c, we get: a=−1;b=2;c=−3
We have a=−1<0
This means the graph is a downward opening parabola.
Also, Discriminant D=b2−4ac ⇒D=22−4×−1×−3⇒D=4−12=−8<0
Thus, the function has a<0 as well as D<0.
So, we can plot the function as: