If a -0 and D -0- then the graph of y - ax 2- bx - c - where -D-b2-4 a cA- lies entirely above x - axisB- touches the X - axisC- lies entirely below x - axisD- cuts the x-axis

The correct option is C lies entirely below x axisFor the equation y=ax^2+bx+c a lt;0⇒ downward opening parabola Given b^2 4ac lt;0 ⇒ D lt;0 ⇒ no real ro ...

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Standard XII

Mathematics

Graph of Quadratic Expression

If a <0 and D...

Question

If $a < 0$ and $D < 0$ , then the graph of $y = a x^{2} + b x + c$
$(where D = b^{2} - 4 a c)$

lies entirely above

x -

axis

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lies entirely below

x -

axis

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cuts the

x -

axis

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touches the

x -

axis

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Solution

The correct option is B lies entirely below $x -$ axis
For the equation
$y = a x^{2} + b x + c$
$a < 0 \Rightarrow$ downward opening parabola
Given
$b^{2} - 4 a c < 0$
$\Rightarrow D < 0 \Rightarrow$ no real roots
The graph of $y = a x^{2} + b x + c$ lies entirely below the $x -$ axis

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Similar questions

Q. Question 18
The point of the form (a, a) always lies on:

A) x-axis
B) y-axis
C) The line y = x
D) The line x + y = 0

The graph of y = a is

(a) the x - axis

(b) the y - axis

(d) a line parallel to x - axis

Q. The point of the form (a, −a), where a ≠ 0, lies on
(a) the x-axis
(b) the y-axis
(c) the line y = x
(d) the line x + y = 0

Q. x = 0 is the equation of
(a) the x-axis
(b) the y-axis
(c) a line parallel to the x-axis
(d) a line parallel to the y-axis

Q. Given some statements regarding the nature of curve obtained while plotting the polynomial

a x^{2} + b x + c

, where

a = - 3, b = 0, c = 0

. Choose the correct statement(s).

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Graph of Quadratic Expression

Standard XII Mathematics

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If a<0 and D<0, then the graph of y=ax2+bx+c (where D=b2−4ac)

The correct option is B lies entirely below x−axisFor the equation y=ax2+bx+c a<0⇒ downward opening parabola Given b2−4ac<0 ⇒D<0⇒ no real roots The graph of y=ax2+bx+c lies entirely below the x−axis

If $a < 0$ and $D < 0$ , then the graph of $y = a x^{2} + b x + c$
$(where D = b^{2} - 4 a c)$

The correct option is B lies entirely below $x -$ axis
For the equation
$y = a x^{2} + b x + c$
$a < 0 \Rightarrow$ downward opening parabola
Given
$b^{2} - 4 a c < 0$
$\Rightarrow D < 0 \Rightarrow$ no real roots
The graph of $y = a x^{2} + b x + c$ lies entirely below the $x -$ axis