Review question

# When does $y=mx-5$ intersect $y=x^2-1$ twice? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5287

## Solution

Find the range of values of $m$ for which the straight line $y=mx-5$ intersects the curve $y=x^2-1$ in two distinct points.

The line meets the curve where

$mx-5=x^2-1,$

which rearranges to

$x^2-mx+4 = 0.$

This has two distinct roots if the discriminant $m^2 -16$ is positive, that is if $m < -4$ or $m > 4$.

This can be written as $\big|m\big|>4$, using the modulus function.