Question

What can you say about the graph of $y=x^2-12x+40$?

• A. Intersects $X$-axis at $1$ point
• B. Intersects $X$-axis at $2$ points
• C. Intersects $X$-axis at $3$ points
• D. Does not intersect $X$-axis at any point

Answer 1

The correct option is D Does not intersect $X$-axis at any point

To find the intersection point of a curve with the $X$-axis, put $y=0$.

$\therefore x^2-12x+40=0$

Calculating the discriminant of the equation,

$\Delta ={12}^2-4\left(40\right)=144-160=-16<0$

Since, $\Delta <0$, the equation has no real roots.

Hence, the curve does not intersect the $X$-axis at any point.