Question

a quadratic function is defined by y=3x^2+4x-2. a linear function is defined by y=mx-5. what value(S) of the slope of the line would make it tangent to the parabola

Answer 1

y=3x²+4x-2

y' is the slope of any tangent line
y'=6x+4

the point of tangency must satisfy both eqaution of the parabola and the the equation of the tangent line.

y=mx-5
3x²+4x-2 = (6x+4)x -5

solve for x
3x²+4x-2 = 6x²+4x - 5
-3x² = -3
x² = 1
x = ±1

for x=1,
y=3(1)²+4(1)-2
y=3+4-2
y=5

subs to y=mx-5
5=m(1)-5
m=10


for x=-1,
y=3(-1)²+4(-1)-2
y=3-4-2
y=-3

subs to y=mx-5
-3=m(-1)-5
m=-2

answers: m = 10, -2

Answer 2

how did you get 6x+4?

Answer 3

hold on what math are you in?

Answer 4

grade 11 functions

Answer 5

ok good. making sure i didnt do it wrong. My teacher went over this exact problem today and i wrote it down. I didnt have time to ask how he actually got the 6x+4 cause of the bell but i am going to tomorrow

Answer 6

oh ok