Quadratic Function (W/ choices. Lesson 2) Flashcards
What is the standard form of a quadratic function?
The standard form of a quadratic function is f(x) = ax² + bx + c.
What does the ‘a’ in the quadratic function equation represent?
‘a’ represents the coefficient that determines the direction and width of the parabola.
True or False: A quadratic function can have at most two real roots.
True.
Fill in the blank: The graph of a quadratic function is called a __________.
parabola.
What are the types of quadratic functions based on the value of ‘a’?
If ‘a’ > 0, the parabola opens upward; if ‘a’ < 0, it opens downward.
What is the vertex form of a quadratic function?
The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.
Multiple choice: Which of the following is NOT a quadratic function? A) f(x) = 2x² + 3x + 1 B) f(x) = x³ + 2 C) f(x) = -x² + 4
B) f(x) = x³ + 2.
What is the axis of symmetry in a quadratic function?
The axis of symmetry is the vertical line x = -b/(2a).
Short answer: How can you find the roots of a quadratic function?
You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Fill in the blank: The discriminant of a quadratic equation is given by __________.
b² - 4ac.
True or False: A quadratic function can have an infinite number of solutions.
False.
What is the maximum or minimum value of a quadratic function?
The maximum or minimum value occurs at the vertex of the parabola.
Multiple choice: If the discriminant is negative, how many real roots does the quadratic function have? A) 0 B) 1 C) 2
A) 0.
What is the general shape of a quadratic function when ‘a’ is positive?
The graph opens upwards.
What does it mean if a quadratic function has two distinct real roots?
It means the graph intersects the x-axis at two points.
Fill in the blank: The value of ‘c’ in the quadratic function f(x) = ax² + bx + c represents the __________.
y-intercept.
True or False: The vertex of a parabola can be found using the formula (h, k) where h = -b/(2a).
True.
What is the role of the coefficient ‘b’ in the quadratic function?
‘b’ influences the position of the vertex along the x-axis.
Short answer: Can a quadratic function have complex roots?
Yes, a quadratic function can have complex roots if the discriminant is negative.
Multiple choice: Which method can be used to solve a quadratic equation? A) Graphing B) Factoring C) Quadratic Formula D) All of the above
D) All of the above.
What is the significance of the vertex in a quadratic function?
The vertex represents the highest or lowest point of the parabola.
Fill in the blank: The roots of the quadratic equation are also known as the __________.
x-intercepts.
True or False: A quadratic function can be expressed in factored form.
True.
Short answer: Give an example of a quadratic function.
An example of a quadratic function is f(x) = 2x² - 4x + 1.
What is the purpose of completing the square in relation to quadratic functions?
Completing the square is used to convert a quadratic function into vertex form.
