You could complete the square to state the vertex.
You could use the quadratic equation to find the roots (which are complex).
Try an example that will require both.
y = x^2 + 2x + 5
Step One
Get the graph. That's included below.
Step Two
Provide the steps for completing the square.
Note: we should get (-1,4)
y= (x^2 +2x ) + 5
y = (x^2 +2x + 1) + 5 - 1
y = (x +1)^2 + 4
The vertex is at (-1,4)
Step Three
Find the roots. Use the quadratic equation. Note that the graph shows us that the equation never crosses or touches the x axis. The roots are complex.

a = 1
b = 2
c = 5




x = -1 +/- 2i
x1 = -1 + 2i
x2 = -1 - 2i And we are done.
The correct answer is 17-x
Answer:
TS and RS
Step-by-step explanation:
Chords are TS and RS
Time taken to reach a person located 5m from the source is 0.2s
<u>Explanation:</u>
Given:
Frequency, f = 10Hz
Wavelength, λ = 2.5m
Distance, d = 5m
Time, t = ?
We know:
velocity = f X λ
v = 10 X 2.5
v = 25 m/s
We know:
Distance = speed X time
On substituting the value we get:
5 = 25 X t
t = 0.2 seconds
Therefore, time taken to reach a person located 5m from the source is 0.2s
Answer:
Step-by-step explanation:
The average scores s (on a 100 point scale) for the students can be modeled by
s = 75 - 6 In(t + 1), 0 < t < 12
where t is the time in months.
a) Since the students were given an exam and then retested monthly with equivalent exams, then,
For the original exam, t = 0
Therefore,
s = 75 - 6 In(0 + 1) = 75 - 6 In1
s = 75 - 6 × 0 = 75
b) the average score after 4 months, t = 4
Therefore,
s = 75 - 6 In(4 + 1) = 75 - 6 In5
s = 75 - 9.66 = 65.34
c) s = 60
Therefore,
60 = 75 - 6 In(t + 1)
6 In(t + 1) = 75 - 60 = 15
In(t + 1) = 15/6 = 2.5
t + 1 = e^2.5 = 12.18
t = 12.18 - 1 = 11.18
t = 11 approximately