Answer:
There is only 1 solution for x.
Step-by-step explanation:
Hi there!
[tex]y = 11x + 5[/tex]
[tex]y = 3x^2 + 5x + 8[/tex]
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:
[tex]3x^2 + 5x + 8= 11x + 5[/tex]
Move everything to the left side:
[tex]3x^2 + 5x + 8-11x-5=0\\3x^2 -6x + 3=0[/tex]
Divide both sides by 3:
[tex]x^2 -2x + 1=0[/tex]
Factor:
[tex](x-1)^2=0[/tex]
Solve for x:
[tex]x-1=0\\x=1[/tex]
Therefore, the only solution for x when y is set equal for both functions is 1. There is only 1 solution for x, so [tex]y = 11x + 5[/tex] is tangent to the curve [tex]y = 3x^2 + 5x + 8[/tex].
I hope this helps!
