Q62 / 125 · BITSAT 2019 · Mathematics

Suppose a parabola $y = a x^{2} + b x + c$ has two $x$ intercepts, one positive and one negative, and its vertex is $(2, - 2)$ , then which of the following is true?

A
$a b > 0$
Correct answer
B
$b c > 0$
C
$a c > 0$
D
$a + b + c > 0$

Solution

Given, $y = a x^{2} + b x + c$ has two $x$ -intercepts one is positive and one is negative and vertex is $(2, - 2)$ . The graph of $y = a x^{2} + b x + c$ is

Clearly from graph

$c > 0$

$- \frac{b}{a} > 0 \Rightarrow - b > 0$

$\Rightarrow b < 0$

$f (1) = a + b + c < 0$

$a b < 0, a c < 0, b c > 0$

Hence, the correct answer is option: 'B'.

More Parabola Questions

If vertex of a parabola is and the equation of its directrix is , then the length of its latus rectum is2023 (Memory Based Paper 2)standard equation of parabola
The parabola having its focus at (3,2) and directrix along the -axis has its vertex at2016standard equation of parabola
The length of the latus-rectum of the parabola whose focus is $ ( {u^2}{2 g} 2 ,- {u^2}{2 g} 2 )$ and directrix is $y= {u^2}{2 g}$, is2011standard equation of parabola
The line $3 x-4 y+7=0$ is rotated through an angle $ { }{4}$ in the clockwise direction about the point $(-1,1)$. The equation of the 2009standard equation of parabola
Let be the length of the common chord of the curves and , and be the length of the latus rectum of , then:2024 (Memory Based Paper 1)Chord of parabola
If the focus of parabola always lies between the lines and then2024 (Memory Based Paper 2)Line and parabola

Suppose a parabola y=ax2+bx+c has two x intercepts, one positive and one negative, and its vertex is (2,-2), then which of the following is true?

Solution

More Parabola Questions

Suppose a parabola $y = a x^{2} + b x + c$ has two $x$ intercepts, one positive and one negative, and its vertex is $(2, - 2)$ , then which of the following is true?