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(B) For a quadratic polynomial $p(x) = ax^{2} + bx + c$,the graph is a parabola.If $a > 0$,the parabola opens upwards.If $a < 0$,the parabola opens do

Vedclass · Accepted Answer

$p(x)=6 x-x^{2}-9$

Vedclass · Answer

(B) For a quadratic polynomial $p(x) = ax^{2} + bx + c$,the graph is a parabola.If $a > 0$,the parabola opens upwards.If $a Let us examine the coefficient of $x^{2}$ for each option:$A) p(x) = x^{2} - 4x + 3$,here $a = 1 > 0$ (opens upwards).$B) p(x) = 6x - x^{2} - 9$,which is $p(x) = -x^{2} + 6x - 9$. Here $a = -1 $C) p(x) = 3 - 6x + 3x^{2}$,here $a = 3 > 0$ (opens upwards).$D) p(x) = x^{2} + 6x + 5$,here $a = 1 > 0$ (opens upwards).Therefore,the correct option is $B$.

Part $I$	Part $II$
$1.$ The graph of $p(x)=x^{2}-5x+6$	$a.$ Intersects the $X$-axis at one point.
$2.$ The graph of $p(x)=x^{2}-10x+25$	$b.$ Intersects the $X$-axis at zero points.
$3.$ The graph of $p(x)=x^{3}-4x$	$c.$ Intersects the $X$-axis at two points.
$4.$ The graph of $p(x)=x^{2}+4x+5$	$d.$ Intersects the $X$-axis at three points.

The graph of $\ldots \ldots \ldots \ldots$ is a curve open downwards.

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