Determine if the quadratic functions are positive definite, negative definite or neither:

Question

a. y=-2x^2+3x+2
b. 3x^2+x+11

Please show work, thank you!

Answer 1

a. opens down; discriminant is positive, so neither (it has real roots)
b. opens up; discriminant is negative, so it does not cross the x-axis -- positive definite

read up on the discriminant and what it means