Question

Which among the following is the correct graphical representation of $y=x^2-3x-4$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Since the coefficient of $x^2$ is positive the parabola will be upward opening parabola, i.e. ; opening towards poistive y-axis.
Given quadratic expression is $y=x^2-3x-4$
On comparing with standard form of quadratic expression $\text{y}=a{x}^2+bx+c$
we get, $a=1,b=-3,c=-4$ and $D=b^2-4ac=(-3{)}^2-\mathrm{4.1.}(-4)=25$
Here, $D>0$ therefore the given quadratic expression have two real roots. Also, we get the roots of the quadratic equation by putting $y=0$
$\Rightarrow y=x^2-3x-4=0$
$\Rightarrow x^2-4x+x-4=0$
$\Rightarrow x(x-4)+1(x-4)=0$
$\Rightarrow (x-4)(x+1)=0$
$\Rightarrow x=4,-1$
From this we can say that parabola cuts the x-axis at $4$ and $-1$.
Hence the correct graph is: