Chapter 2: Quadratics Flashcards
How do you solve a quadratic expression by factorising?
1) Write the equation in the form ax² + bx + c = 0.
2) Factorise the left-hand side.
3) Set each factor equal to zero and solve to find the value(s) of x.
What is the quadratic formula of quadratic equation ax² + bx + c = 0?
x = (-b ±√(b² - 4ac))/2a
What is the formula for completing the square?
x² + bx = (x + (b/2))² -(b/2)²
What is the formula for completing the square of a quadratic equation?
ax² + bx + c = a(x + (b/2a)² +(c - (b²/4a))
What is the domain?
The set of possible inputs for a function (x)
What is the range?
The set of possible outputs for a function (y)
What are the roots of a function?
The values of x for which f(x) = 0
How do you find the turning point of a quadratic graph?
If f(x) = a(x + p)² + q, the graph of y = f(x) have a turning point of (-p, q).
What is the discriminant?
b² - 4ac of the quadratic formula (without the square root)
What does it mean if b² - 4ac > 0?
It has 2 distinct real roots.
What does it mean if b² - 4ac = 0?
It has one repeated root
What does it mean if b² - 4ac < 0
It has no real roots
