Bellwork
Use the distributive
property to find each
product.
1. (x+2)(x -5)
2. (-3x+2)(2x-6)
State whether the parabola
opens up or down and
whether the y-coordinate of
the vertex is the minimum
value or maximum value of
the function. Then, find
the coordinates of its
vertex.
Identify whether each function
5. f(x) =(3-x)(2+x)
is quadratic.
6. f(x) = 4 – x + x²
3. f(x) = 4x³ - 8x²
2x
4. f(x)= -2x + 8
Lesson 5.2
Introduction to Solving Quadratic Equations
Notes on Lesson 5.2 Solving Quadratic Equations
Solving Equations of the Form x² = a
If a≥ 0, then x =
or x = EXAMPLE #1
4x² + 13 = 253
Exact Answer: x = ±
Approximate Answer: x≈7.75
Notes on Lesson 5.2 Solving Quadratic Equations
Solving Equations of the Form x² = a
If a≥ 0, then x =
or x = EXAMPLE #2
9(x-2)² = 121
Notes on Lesson 5.2 Solving Quadratic Equations
Solving Equations of the Form x² = a
If a≥ 0, then x =
or x = EXAMPLE #3
7(x+1)² = 161
Exact Answer:
Approximate Answer:
#1) x²-12 = 4
Answer: x = ±4
#2) 5x²- 4 = 96
Exact Answer: x = ±
Approximation: x≈ 4.47
#3) 6x² + 15 = 23
#4) 12= 4(x-2)² - 8
What if a there is a negative under the
square root?
 It isn’t that Complex…We will use our imaginations!!!!
Example
x  1
2
x  121
2
x 53
2
What if a there is a negative under the
square root?
 It isn’t that Complex…We will use our imaginations!!!!
Example
x  1
2
x   121
2
x 53
2
Using the Pythagorean Theorem
If ABC is a right triangle with the right angle at C, then a²+b²=c²
Parts of a right triangle.
Hypotenuse (c)
Side
(a)
Side (b)
Practice:
Find the unknown length in each right triangle. Give answers to
the nearest tenth.
Solution:
x

7cm
9cm
a² +b² = c²
7² + 9² = c²
49 + 81 = c²
130 = c²
c≈11.4 cm
Practice:
Find the unknown length in each right triangle. Give answers to
the nearest tenth.
Solution:
13cm

6cm
x
a² +b² = c²
6² + b² = 13²
36 + b² = 169
c² = 133
c≈11.5 cm
Worksheet 5.2A