Question

Show that y = 11x + 5 is a tangent to the curve y = 3x² + 5x + 8

Answer 1

Answer:

There is only 1 solution for x.

Step-by-step explanation:

Hi there!

$y = 11x + 5$

$y = 3x^2 + 5x + 8$

This is a linear-quadratic system. If the line is tangent to the parabola, it means that it would only have 1 solution.

Set y equal:

$3x^2 + 5x + 8= 11x + 5$

Move everything to the left side:

$3x^2 + 5x + 8-11x-5=0\\3x^2 -6x + 3=0$

Divide both sides by 3:

$x^2 -2x + 1=0$

Factor:

$(x-1)^2=0$

Solve for x:

$x-1=0\\x=1$

Therefore, the only solution for x when y is set equal for both functions is 1. There is only 1 solution for x, so $y = 11x + 5$ is tangent to the curve $y = 3x^2 + 5x + 8$.

I hope this helps!