Factorising and Completing the square Flashcards
What is the standard form of a quadratic equation?
The standard form is ax^2 + bx + c = 0.
True or False: The coefficient ‘a’ in a quadratic equation can be zero.
False.
Fill in the blank: The process of expressing a quadratic expression as a product of its factors is called _______.
factorising.
What is the first step in factorising a quadratic expression of the form ax^2 + bx + c?
Identify a, b, and c.
What do you call the two numbers that multiply to give ‘ac’ and add to give ‘b’ when factorising?
The factors.
True or False: Completing the square can be used to solve quadratic equations.
True.
What is the formula for completing the square for the expression x^2 + bx?
x^2 + bx = (x + b/2)^2 - (b/2)^2.
Multiple Choice: Which of the following is a correct factorisation of x^2 + 5x + 6? A) (x + 2)(x + 3) B) (x + 1)(x + 6) C) (x + 3)(x + 2)
A) (x + 2)(x + 3) and C) (x + 3)(x + 2) are correct.
What is the vertex of the parabola represented by the equation y = a(x - h)^2 + k?
The vertex is the point (h, k).
Fill in the blank: The quadratic formula is used to find the _______ of a quadratic equation.
roots.
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / (2a).
True or False: The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation.
True.
What does it mean if the discriminant is positive?
There are two distinct real roots.
What does it mean if the discriminant is zero?
There is one real root (a repeated root).
What does it mean if the discriminant is negative?
There are no real roots (the roots are complex).
Fill in the blank: To complete the square for the expression x^2 + 6x, you add and subtract ______.
9.
What is the completed square form of the expression x^2 + 4x - 5?
(x + 2)^2 - 9.
Multiple Choice: Which of the following is a factor of x^2 - 9? A) (x - 3) B) (x + 3) C) Both A and B
C) Both A and B.
True or False: The expression x^2 + 2x + 1 can be factorised as (x + 1)(x + 1).
True.
What is the first step in factorising the expression x^2 - 10x + 24?
Find two numbers that multiply to 24 and add to -10.
What is the factored form of x^2 - 4?
(x - 2)(x + 2).
Fill in the blank: The expression x^2 + 8x + 16 can be written in completed square form as ______.
(x + 4)^2.
What is the value of ‘h’ in the vertex form y = a(x - h)^2 + k for the function y = 2(x - 3)^2 + 5?
3.
True or False: A quadratic function can have at most two x-intercepts.
True.
What is the axis of symmetry for the parabola represented by the equation y = ax^2 + bx + c?
x = -b/(2a).
