Question

The graph of the quadratic polynomial $a{x}^2+bx+c,a\ne 0$ is always

• A. straight line
• B. parabola
• C. circle
• D. None of these

Answer 1

The correct option is B parabola

Let $a{x}^2+bx+c=y\Rightarrow x^2+\frac{b}{a}x+\frac{c}{a}=\frac{y}{a}\Rightarrow x^2+2\frac{b}{2a}x+{\left(\frac{b}{2a}\right)}^2=\frac{y}{a}+{\left(\frac{b}{2a}\right)}^2\Rightarrow {(x+\frac{b}{2a})}^2=\frac{y}{a}+{\left(\frac{b}{2a}\right)}^2\Rightarrow X^2=Y$

$X=f\left(x\right)\&Y=f\left(y\right).$

So it s an equation of a parabola.

The graph will be that of a parabola.