unit 6 - Quadratic functions Flashcards
What is the standard form of a quadratic function?
y = ax^2 + bx + c
In the function y = ax^2 + bx + c, what does ‘a’ determine?
‘a’ determines the direction and width of the parabola.
True or False: A quadratic function can only have one x-intercept.
False
What is the vertex of a parabola?
The vertex is the highest or lowest point on the graph of a quadratic function.
Fill in the blank: The axis of symmetry for a quadratic function in standard form is given by x = ____.
-b/(2a)
What shape does the graph of a quadratic function create?
A parabola
What are the roots of a quadratic function?
The values of x where the function equals zero.
True or False: The quadratic formula can be used to find the roots of any quadratic equation.
True
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / (2a)
What does the discriminant (b² - 4ac) tell us about the roots of a quadratic function?
It indicates the number and type of roots.
If the discriminant is positive, how many real roots does the quadratic function have?
Two distinct real roots.
If the discriminant is zero, how many real roots does the quadratic function have?
One real root (a repeated root).
If the discriminant is negative, how many real roots does the quadratic function have?
No real roots (two complex roots).
What is the vertex form of a quadratic function?
y = a(x - h)² + k
In the vertex form y = a(x - h)² + k, what do ‘h’ and ‘k’ represent?
‘h’ is the x-coordinate and ‘k’ is the y-coordinate of the vertex.
What does it mean for a quadratic function to be ‘concave up’?
The parabola opens upwards, and ‘a’ is positive.
What does it mean for a quadratic function to be ‘concave down’?
The parabola opens downwards, and ‘a’ is negative.
True or False: The y-intercept of a quadratic function is found by setting x = 0.
True
What is the y-intercept of the quadratic function y = 2x² + 3x + 5?
5
Fill in the blank: The maximum or minimum value of a quadratic function occurs at the _____ of the parabola.
vertex
What is the axis of symmetry for the function y = 3x² - 6x + 2?
x = 1
What is a real-world example of a quadratic function?
The path of a thrown ball or the shape of a satellite dish.
What is the effect of increasing the value of ‘a’ in y = ax²?
The parabola becomes narrower.
True or False: The roots of a quadratic function are always real numbers.
False
What is the standard form of a quadratic function?
y = ax^2 + bx + c
In the function y = ax^2 + bx + c, what does ‘a’ determine?
‘a’ determines the direction and width of the parabola.
True or False: A quadratic function can only have one x-intercept.
False
What is the vertex of a parabola?
The vertex is the highest or lowest point on the graph of a quadratic function.
Fill in the blank: The axis of symmetry for a quadratic function in standard form is given by x = ____.
-b/(2a)
What shape does the graph of a quadratic function create?
A parabola
What are the roots of a quadratic function?
The values of x where the function equals zero.
True or False: The quadratic formula can be used to find the roots of any quadratic equation.
True
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / (2a)
What does the discriminant (b² - 4ac) tell us about the roots of a quadratic function?
It indicates the number and type of roots.
If the discriminant is positive, how many real roots does the quadratic function have?
Two distinct real roots.
If the discriminant is zero, how many real roots does the quadratic function have?
One real root (a repeated root).
If the discriminant is negative, how many real roots does the quadratic function have?
No real roots (two complex roots).
What is the vertex form of a quadratic function?
y = a(x - h)² + k
In the vertex form y = a(x - h)² + k, what do ‘h’ and ‘k’ represent?
‘h’ is the x-coordinate and ‘k’ is the y-coordinate of the vertex.
What does it mean for a quadratic function to be ‘concave up’?
The parabola opens upwards, and ‘a’ is positive.
What does it mean for a quadratic function to be ‘concave down’?
The parabola opens downwards, and ‘a’ is negative.
True or False: The y-intercept of a quadratic function is found by setting x = 0.
True
What is the y-intercept of the quadratic function y = 2x² + 3x + 5?
5
Fill in the blank: The maximum or minimum value of a quadratic function occurs at the _____ of the parabola.
vertex
What is the axis of symmetry for the function y = 3x² - 6x + 2?
x = 1
What is a real-world example of a quadratic function?
The path of a thrown ball or the shape of a satellite dish.
What is the effect of increasing the value of ‘a’ in y = ax²?
The parabola becomes narrower.
True or False: The roots of a quadratic function are always real numbers.
False
