Math Exam Flashcards
What is a quadratic function?
A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c.
True or False: The graph of a quadratic function is a straight line.
False
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 formula represent?
‘a’ represents the coefficient of the x² term in the quadratic function.
Fill in the blank: The graph of a quadratic function is called a __________.
parabola
What are the x-intercepts of a quadratic function?
The x-intercepts are the points where the graph intersects the x-axis, which occur when f(x) = 0.
True or False: A parabola opens upwards if the coefficient ‘a’ is positive.
True
What is the vertex of a parabola?
The vertex is the highest or lowest point on the graph of a parabola, depending on its orientation.
What is the axis of symmetry in a quadratic function?
The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.
Fill in the blank: The maximum or minimum value of a quadratic function occurs at the __________.
vertex
What is the general shape of a parabola that opens downwards?
The general shape is a downward-facing U.
True or False: The discriminant of a quadratic equation can determine the number of real roots.
True
What is the discriminant in the context of a quadratic function?
The discriminant is given by the formula b² - 4ac and indicates the nature of the roots of the quadratic equation.
What does it mean if the discriminant is positive?
If the discriminant is positive, the quadratic equation has two distinct real roots.
What does it mean if the discriminant is zero?
If the discriminant is zero, the quadratic equation has exactly one real root, also known as a repeated root.
What does it mean if the discriminant is negative?
If the discriminant is negative, the quadratic equation has no real roots, only complex roots.
Fill in the blank: The point where the graph of the quadratic function touches the x-axis is called a __________.
root
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.
What does the ‘k’ in vertex form represent?
‘k’ represents the y-coordinate of the vertex of the parabola.
True or False: The roots of a quadratic function can be found using factoring.
True
What is the significance of the y-intercept in a quadratic function?
The y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0.
Fill in the blank: The __________ of a quadratic function is the highest or lowest point on the graph.
vertex
What is the relationship between the coefficients and the roots of a quadratic function?
The relationships are defined by Vieta’s formulas, which relate the sum and product of the roots to the coefficients.
True or False: A quadratic function can have at most two real roots.
True
What are the two ways to graph a quadratic function?
A quadratic function can be graphed using a table of values or by identifying the vertex and intercepts.
What is the importance of understanding quadratics in mathematics?
Understanding quadratics is crucial for solving various real-world problems and for advanced studies in algebra, calculus, and physics.
What is the typical domain of a quadratic function?
The domain of a quadratic function is all real numbers, expressed as (-∞, ∞).
Fill in the blank: The range of a quadratic function that opens upwards is __________.
from the vertex’s y-coordinate to infinity.
What is the effect of changing the value of ‘a’ in the quadratic function?
Changing the value of ‘a’ affects the width and direction of the parabola.
What happens to the parabola if ‘a’ is negative?
If ‘a’ is negative, the parabola opens downwards.
