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Mitchell District High School
MPM 2D Principles of Mathematics
Unit 6: Quadratic Equations Unit Goals:
1) I can understand the difference between a quadratic function and an equation
2) I can use graphs of quadratic functions so solve corresponding quadratic equations.
3) I can solve quadratic equations by algebraic methods, including using the quadratic formula.
4) I can model real life situations with quadratic equations and solve problems with them.
# Topic Goal Practice
questions Questions to Ask About
1 Solving Quadratic
Equations by Graphing
I know the difference between a function and an equation and I can use the graph of a function, so solve
for a given quadratic equation.
Page 275 #1-3eop,16, 18-20
2 Solving Quadratic
Equations by Factoring.
I can solve a quadratic equation by factoring.
Page 282 #(3, 4, 5, 8,9)eop
3 The Quadratic Formula.
I know how the quadratic formula was derived and I can use it to solve
any quadratic equation.
Page 292 #1-3, 5, 6
4 Kinds of Roots
I can explain the relationship between different kinds of roots of Quadratic equations, the quadratic
formula and the corresponding function.
Page 295 #20, 21, 23, 24, 25
5 Applications of
Quadratic Equations – Part 1
I can apply what I know about quadratic equations and functions to solve problems with real world
applications.
Page 275 #4, 5, 6, 7, 9, 10, 12
6 Applications of
Quadratic Equations – Part 2
I can apply what I know about quadratic equations and functions to solve problems with real world
applications.
Page 283 #12, 21, 25, 26, 27,
33, 34 Page 293
#8, 10, 13, 14, 15, 17, 18
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MPM 2D U6L4 Kinds of Roots
Kinds of Roots for Quadratic EquationsSolve each of the following quadratic equations using the quadratic formula
Example 1. _____________________Roots
What does theparabola look like?
x
y
6x2 - x = 2
Kind of Root?
What part of the solution
determines this?
Example 2. _____________________Roots
What does theparabola look like?
x
y
8x2 + 1 - 3x = 5x - 1
Kind of Root?
What part of the solution
determines this?
Topic : Quadratic Equations
Goal : to discover the relationship between different kinds of roots of quadratic equations, the quadratic formula and the corresponding quadratic function.
MPM 2D U6L4 Kinds of Roots
Example 3. _____________________Roots
5x2 + 3x + 5 = 3x2
Kind of Root?
Example 4. _____________________Roots
What does theparabola look like?
x
y
5(x - 2)2 = 26 - 17x
Kind of Root?
What part of the solution
determines this?
What part of the solution
determines this?
What does theparabola look like?
x
y
MPM 2D U6L4 Kinds of Roots
Kind of Roots
The part under the square root (b2-4ac) is called the descriminant
It determines what kinds of roots you have.
DescriminantCorresponding
Function
Two RationalRoots
Two Irrational Roots
No RealRoots
(Complex Roots)
Equal Roots
b2-4ac
b2-4ac
b2-4ac
b2-4ac
y
x
y
x
y
x
Homework Page 295 # 20, 21, 23, 24, 25
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MPM 2D U6L6 Applicaitons of Quadratic Equations Part 2
Applications of Quadratic Equations Part 2More types of questions...
Example 4. As one value increases the other decreases (Revenue/Yield)
The student council sells sweatshirts as a fundraiser. Last year they sold 325 shirts at $45 each. In an effort to promote school spirit, this year they intend to decrease the price. A survey shows that for each $1 decrease, they will sell 5 more shirts.
a) What selling price will result in a $13 125 revenue?b) How many shirts will be sold at this price?
MPM 2D U6L6 Applicaitons of Quadratic Equations Part 2
A picture that is 20 cm x 25 cm is cropped so that twice the width is taken from the bottom as from the right side. If the area cropped of is 100 cm2, what width is cropped from each side?
Example 5. Dimension changes.
Page 283 #12, 21, 25, 26, 27, 33, 34Page 293 #8, 10, 13, 14, 15, 17, 18
You don't have to complete them all, but make sure you look at them all, and complete several different kinds!
Quadratic Equations 1. We know that the roots of a quadratic equation are the same as the x-intercepts (zeros) of the function that we
get if we replace the zero in a quadratic equation with a y. Describe the kinds of roots of quadratic equations using the cooresponding functions as references.
2. Complete the square for
€
−2x 2 + 8x + c = 0 and use what you know about the cooresponding function to determine the value of c that will result in a) Equal Roots, b) Complex Roots (no real roots) and c) Two Real Roots.
3. State the solutions to the following quadratic equations that are ALREADY in factored form.
a)
€
(x + 2)(x + 5) = 0 b)
€
(x − 6)(2x + 3) = 0 c)
€
(3x + 4)(5x − 7) = 0 d)
€
2x(3x + 9) = 0 4. Solve the following quadratic equations by factoring.
a)
€
4x 2 −16x = 0 b)
€
x 2 + 5x + 4 = 0 c)
€
3x 2 + 36x + 49 = 8x d)
€
6x 2
5−2x4
= 0
e)
€
3m2 = −16m − 21 f)
€
3x 2 +14x − 49 = 0 g)
€
3x 2 − 4 = −8x −1 h)
€
2x 2 − 50 = 0
i)
€
x 2 − 7x2
+32
= 0 j)
€
x 2
2−5x4
= 3 k)
€
5x 2 = −2x l)
€
x 2 +11= 300
5. Solve using the quadratic formula. Round your answers to the nearest hundredth if necessary, otherwise
leave as a fraction.
a)
€
5x 2 − 8x − 4 = 0 b)
€
4x 2 − 20x + 25= 0 c)
€
x 2 +14x + 9 = 0 d)
€
19− 4x 2 = 2
e)
€
(2x + 3)2 − 6 = 11x + 8 f)
€
2x(x − 6) = 3x + 9
6. The path of a thrown ball can be represented by the relation
€
h = −0.007d 2 + 0.4d +1.5 , where d is the horizontal distance traveled in metres and h is the height in metres. What is the horizontal distance the ball travels before it hits the ground?
7. A walkway around a 6 m by 9 m lawn is the same width on all 4 sides. If the area of the walkway is the same as
the area of the lawn, how wide is the walkway? 8. A football is punted, and its path is modeled by the function
€
h = −0.1d 2 + 3.4d + 8 , where h metres is the height of the football and d metres is the horizontal distance from the line of scrimmage. Find, to the nearest metre, how far the punt travels from the line until it first hits the ground.
9. The area of a rectangle is 560 square inches. The length is 3 more than twice the width. Find the length and the
width. 10. In a right angle triangle the base is 3 cm less than the height and the hypotenuse is 4 cm. What are the base
and height? 11. The area of a triangle is 32 cm2. If the base is 2 cm shorter than triple the height, what are the dimensions of
the triangle?
12. A sticker warehouse sells an average of 6 rolls of stickers per customer at $4 per roll. Statistics show that for every $0.25 decrease in price, customers will buy an additional roll.
(a) According to this model, if the stickers were reduced to $3 per roll, what will be the revenue? (b) According to this model, at what sticker price will the revenue from stickers be $28.""
13. A sporting goods store sells 90 ski jackets in a season for $200 each. Each $10 decrease in the price would
result in five more jackets being sold. Find the number of jackets sold and the selling price to give revenues of $17 600 from sales of ski jackets.
14. Eduardo works in the “remodeling” division at a modern art museum. One of his jobs is to keep the different
metal sculptures painted and in good condition. One outdoor sculpture has the shape of a large right triangle. Eduardo needs to know the area of the triangle so that he can figure out how much paint it will need. He finds out that the area he needs to paint is 10 square feet. If the longer leg is 3 feet less than twice the shorter leg, what are the lengths of the two legs?
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