MCQ
Fig. show the graph of the polynomial $f(x) = ax^2+ bx + c$ for which :
- A$a < 0, b > 0$ and $c > 0$
- ✓$a < 0, b < 0$ and $c > 0$
- C$a < 0, b < 0$ and $c < 0$
- D$a > 0, b > 0$ and $c < 0$
✓
Answer
Correct option: B.
$a < 0, b < 0$ and $c > 0$
Clearly, $f(x) = ax^2+ bx + c$ represent a parabola opening downwards.
Therefore $, a < 0 y = ax^2 + bx + c $ cuts $y-$ axis at $P$ which lies on $OY$.
Putting $x = 0$ in $y = ax^2+ bx + c$, we get $y = c$.
So the coordinates $P$ are $(0, c).$ Clearly, $P$ lies on $OY$.
Therefore $c > 0$
The vertex $\Big(\frac{-\text{b}}{2\text{a}},\frac{-\text{D}}{4\text{a}}\Big)$ of the parabola is in the second quadrant.
Therefore $\frac{-\text{b}}{2\text{a}}<0,\text{b}<0$
Therefore $a < 0, b < 0,$ and $c > 0$
Hence, the correct choice is $(b)$
Therefore $, a < 0 y = ax^2 + bx + c $ cuts $y-$ axis at $P$ which lies on $OY$.
Putting $x = 0$ in $y = ax^2+ bx + c$, we get $y = c$.
So the coordinates $P$ are $(0, c).$ Clearly, $P$ lies on $OY$.
Therefore $c > 0$
The vertex $\Big(\frac{-\text{b}}{2\text{a}},\frac{-\text{D}}{4\text{a}}\Big)$ of the parabola is in the second quadrant.
Therefore $\frac{-\text{b}}{2\text{a}}<0,\text{b}<0$
Therefore $a < 0, b < 0,$ and $c > 0$
Hence, the correct choice is $(b)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The probability of getting an even number, when a die is thrown once, is :
The probability that a leap year selected at random will have $53$ Fridays is :
→The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
If $\text{x}=\text{a}\sec\theta\cos\phi,\text{y}=\text{b}\sec\theta\sin\phi$ and ${z}=\text{c}\tan\theta,$ then $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=$
→If two of the zeros of the cubic polynomial $ax^3 + bx^2 + cx + d$ are each equal to zero, then the third zero is:
→The area of the sector of a circle of radius $10.5 \ cm$ is $69.3 \ cm^2$. Find the central angle of the sector.
→The decimal expansion of $\pi$ :
→In a data, if $l =40, h=15, f _1=7, f _0=3, f _2=6$, then the mode is
→By Euclid’s division lemma $x = qy + r, x > y$ the value of $q$ and $r$ for $x = 27$ and $y = 5$ are :
→$\triangle \text{ABC}\sim\triangle\text{DEF}, \text{ar}(\triangle\text{ABC})=9\text{ cm}^2,\ \text{ar} (\triangle\text{DEF})=16\text{ cm}^2.$ If $BC = 2.1\ cm,$ then the measure of $EF$ is :
→