Algebra 2
Notes – Lesson 5.2
1. Properties of Parabolas
Remember the standard form for a quadratic function: 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
When 𝒂 > 𝟎
 The parabola opens _____________________.
 The vertex is a _______________________.
When 𝒂 < 𝟎
 The parabola opens ___________________.
 The vertex is a _______________________.
2. Important Points of a Parabola
The y – intercept of the function happens when _____________________________________.
The equation for the line of symmetry is _________________________.
This equation also gives you ____________________________________________________. To find the y-value
of the vertex, plug in the number you found for x and solve for y.
**THE VALUE OF THE MAXIMUM/MINIMUM IS GIVEN BY THE Y-VALUE OF THE VERTEX**
Examples:
Find the vertex and the y-intercept of each quadratic equation. Use those points to graph the function (reflect to
get the other points!)
a) 𝑦 = 𝑥 2 − 2𝑥 − 3
b)
𝑦 = −𝑥 2 + 4𝑥 + 2
8
8
6
6
4
4
2
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-8 -7 -6 -5 -4 -3 -2 -1
-2
-2
-4
-4
-6
-6
-8
-8
1 2 3 4 5 6 7 8
Algebra 2
Notes – Lesson 5.2
c) 𝑦 = 𝑥 2 + 3
d)
1
𝑦 = − 4 𝑥 2 + 2𝑥
8
8
6
6
4
4
2
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-8 -7 -6 -5 -4 -3 -2 -1
-2
-2
-4
-4
-6
-6
-8
-8
1 2 3 4 5 6 7 8
e) Your small business determines that profits are maximized with the following equation:
𝑦 = −2𝑥 2 + 15𝑥 + 5
x = workers employed
y = profit (in thousand $)
What number of workers will give the company the MOST profit (maximum)? What is that profit?
f) A lighting fixture manufacturer has daily production of 𝐶 = 0.25𝑛2 − 10𝑛 + 800, where C is the total
daily cost in dollars and n is the number of light fixtures produced. How many fixtures should be
produced to yield a minimum cost?