Quadratic functions

Question 1

How to find the minimum/maximum of f(x)=a(x-h)²+k?

Answer 1

If a>0 the minimum is (h,k)
If a<0 the maximum is (h,k)

Question 2

What is the discriminant of f(x)=ax²+bx+c?

Answer 2

b²-4ac

Question 3

What if the discriminant is >0?

Answer 3

There are 2 real roots or two points of intersection

Question 4

What if the discriminant is =0?

Answer 4

There are 2 equal roots or one point of intersection

Question 5

What if the discriminant is <0?

Answer 5

There are no real roots or no points of intersection

Question 6

Find the values of k for which y=kx+2 is a tangent to y=3x²+x+5?

Answer 6

3x²+x+5=kx+2
3x²+(1-k)x+3=0
(1-k)²-433=0
1-2k+k²-36=0
k²-2k-35=0
(k+5)(k-7)=0
k=-5 or k=7