Question
2. Without graphing determine the number of zeros for each function. a) f(x)=x^2-2x-14 b) g(x)=-3x^2+0.06x+4 c) f(x)=(1)/(4)x^2-3x+9 d) f(v)=-v^2+2v-1 e) f(x)=(1)/(2)x^2-x+(5)/(2) f) g(y)=-6y^2+5y-1
Solution
4.3
(116 Votes)
Aidan
Veteran ยท Tutor for 9 years
Answer
### a) Two zeros### b) Two zeros### c) One zero### d) One zero### e) No real zeros### f) Two zeros
Explanation
## Step 1: Calculate the Discriminant### The number of zeros of a quadratic function
is determined by the discriminant,
. If the discriminant is positive, there are two distinct real zeros. If the discriminant is zero, there is one real zero (a repeated root). If the discriminant is negative, there are no real zeros.## Step 2: Calculate Discriminant for a)
###
,
,
. Discriminant
. Two real zeros.## Step 3: Calculate Discriminant for b)
###
,
,
. Discriminant
. Two real zeros.## Step 4: Calculate Discriminant for c)
###
,
,
. Discriminant
. One real zero.## Step 5: Calculate Discriminant for d)
###
,
,
. Discriminant
. One real zero.## Step 6: Calculate Discriminant for e)
###
,
,
. Discriminant
. Two real zeros.