Quadratics Flashcards
(26 cards)
What is the first step to solve a quadratic equation by factorising?
Write the equation in the form ax² + bx + c = 0
After factorising the left-hand side of a quadratic equation, what should you do next?
Set each factor equal to zero and solve to find the value(s) of x
What formula gives the solutions of the equation ax² + bx + c = 0 where a ≠ 0?
-b ± √(b² - 4ac) / 2a
What is the set of possible inputs for a function called?
Domain
What is the set of possible outputs of a function called?
Range
What are the roots of a function?
The values of x for which f(x) = 0
How can you find the coordinates of a turning point of a quadratic graph?
By completing the square
If f(x) = a(x + p)² + q, where is the turning point located?
At (-p, q)
What is the expression b² - 4ac called in a quadratic function?
Discriminant
What does a discriminant value of b² - 4ac > 0 indicate?
Two distinct real roots
What does a discriminant value of b² - 4ac = 0 indicate?
One repeated real root
What does a discriminant value of b² - 4ac < 0 indicate?
No real roots
Can quadratics be used to model real-life situations?
Yes
What is the first step to solve a quadratic equation by factorising?
Write the equation in the form ax² + bx + c = 0
After factorising the left-hand side of a quadratic equation, what should you do next?
Set each factor equal to zero and solve to find the value(s) of x
What formula gives the solutions of the equation ax² + bx + c = 0 where a ≠ 0?
-b ± √(b² - 4ac) / 2a
What is the set of possible inputs for a function called?
Domain
What is the set of possible outputs of a function called?
Range
What are the roots of a function?
The values of x for which f(x) = 0
How can you find the coordinates of a turning point of a quadratic graph?
By completing the square
If f(x) = a(x + p)² + q, where is the turning point located?
At (-p, q)
What is the expression b² - 4ac called in a quadratic function?
Discriminant
What does a discriminant value of b² - 4ac > 0 indicate?
Two distinct real roots
What does a discriminant value of b² - 4ac = 0 indicate?
One repeated real root
