Question

The graph of $p\left(x\right)=x^2-4x+3$ represents _____

• A. a line segment
• B. parabola
• C. a line
• D. a ray

Answer 1

The correct option is B parabola

$p\left(x\right)=x^2-4x+3$

Finding the y-intercept

To find y-intercept of graph of p. We can find $p\left(0\right)$

$p\left(x\right)=x^2-4x+3$

$p\left(0\right)=(0{)}^2-4(0)+3$

$P\left(0\right)=3$

The y-intercept of graph of $y=p\left(x\right)$ is $(0,3)$

Find the x-intercept

To find x-intercept, we can solve equation $p\left(x\right)=0$

$0=x^2-4x+3$

Solving the above equation, we get

$x=3$, $x=1$

The x-intercept of graph of $y=p\left(x\right)$ are $(3,0)$ & $(1,0)$

The leading term of the polynomial is $x^2$, & so the end behaviour of function p will be the same as the end behaviour of $x^2$.

Since degree is even & the leading coefficient is positive, the end behaviour will be:

$x\to +\infty$, $f\left(x\right)\to +\infty$

$x\to -\infty$, $f\left(x\right)\to +\infty$.