Solve By Factoring
What are the different types of factoring?
Common factoring, Simple trinomial Factoring, Complex trinomial factoring, factor by grouping, Prefect square trinomial, difference of squares binomial,
What is the purpose of completing the square?
The purpose of completing the square is to rewrite a quadratic equation in the form y = (x + h)2 + k which makes it easier to state the vertex
What is the quadratic formula?
x = -b土√b2 - 4ac / 2a
What is the discriminant formula?
b2 - 4ac
The solutions of a quadratic equation can have different interpretations based on the context. True or False?
True
Factor the quadratic equation: x2 + 5x + 6
(x + 2)(x + 3)
Complete the square for the quadratic equation:
x2 + 8x - 7
y=(x + 4)2 - 23
The quadratic formula can be used to solve any quadratic equation, even ones that cannot be factored. True or False?
True
Describe the roots of the equation ax2+ bx + c = 0 in each of the following situations. Explain and justify your reasoning.
b2 − 4ac = 0
b2 − 4ac > 0 (positive)
b2 − 4ac < 0 (negative)
= 0: one solutions
negative: no solutions
positive" two solutions
A ball is thrown into the air with an initial velocity of 20 m/s. The height of the ball can be modeled by the equation h = -5t^2 + 20t + 2. What do the solutions of this equation represent?
The solutions represent the times when the ball reaches a certain height or hits the ground.
Factor the quadratic equation: x2 - 9
(x - 3)(x + 3)
Complete the square for the quadratic equation:
x2 + 6x + 4
y = (x + 3)2 - 5
Solve the quadratic equation using the quadratic formula: x2 + 7x + 12 = 0
x = -4, x = -3
Use the discriminant to determine the number of solutions each quadratic equation would have.
x2 − 4x + 4 = 0
1 solution
The path of a golf ball can be modelled by the equation ℎ = −2d2 + 12d − 13, where d represents the horizontal distance, in metres, that the ball travels and ℎ represents the height of the ball, in metres, above the ground. What is the maximum height of the golf ball and at what horizontal distance does it occur?
The max height of 5m occurs at a horizontal distance of 3m
Solve the quadratic equation by factoring:
-x2 - 4x + 5
x = -5, x = 1
Solve the quadratic equation by completing the square: x2 - 10x + 21 = 0
x = 3, x = 7
Solve the quadratic equation using the quadratic formula: 2x2 - 5x - 3 = 0
x = -1, x = 3/2
Use the discriminant to determine the number of solutions each quadratic equation would have.
-2x2 + 3x - 8 = 0
No real solutions
The area of the front cover of a daily journal is 273 cm2, and the length is 8 cm greater than the width. What are the dimensions of the cover
13 cm by 21 cm
Solve the following equation by factoring:
4x2 + 12x = −9
x = -2/3
A quadratic equation in vertex form is written as y = a(x - h)2 + k. What does each term represent?
a represents the coefficient of the quadratic term, h represents the x-coordinate of the vertex, and k represents the y-coordinate of the vertex.
Solve the quadratic equation using the quadratic formula: 3x2 + 4x - 1 = 0
x = -2/3, x = 1
Use the discriminant to determine the number of solutions each quadratic equation would have.
2x2 + 3x - 8 = 0
2 solutions
A rectangular lawn measuring 8 meters by 4 meters is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165 m2. What is the width of the flower bed?
x = 3.5m