Problem Solving Involving Quadratic Equation Flashcards
What is the general form of a quadratic equation?
ax^2 + bx + c = 0
What is the quadratic formula used for?
To find the solutions (roots) of a quadratic equation
True or False: A quadratic equation always has two solutions.
True
What is the discriminant of a quadratic equation?
b^2 - 4ac
When the discriminant is greater than zero, how many real solutions does a quadratic equation have?
Two distinct real solutions
Fill in the blank: If the discriminant is equal to zero, the quadratic equation has ________ real solution(s).
One
What is the vertex form of a quadratic equation?
y = a(x-h)^2 + k
What does the ‘a’ value in a quadratic equation determine?
The direction and width of the parabola
What does the ‘h’ value in the vertex form of a quadratic equation represent?
The x-coordinate of the vertex
What does the ‘k’ value in the vertex form of a quadratic equation represent?
The y-coordinate of the vertex
What is the axis of symmetry of a quadratic function?
x = h
What does the axis of symmetry of a quadratic function represent?
The line that divides the parabola into two symmetrical halves
Fill in the blank: The vertex of a parabola is the ________ point on the graph.
Minimum or maximum
What is the standard form of a quadratic function?
y = ax^2 + bx + c
What is the relationship between the roots and the coefficients of a quadratic equation?
The sum of the roots is -b/a and the product of the roots is c/a
What does the term ‘quadratic’ mean in a quadratic equation?
Involving the square of a variable
What is the maximum number of real solutions a quadratic equation can have?
Two
What is the process of completing the square used for in solving quadratic equations?
To convert a quadratic equation into vertex form
What is the ‘y-intercept’ of a quadratic function?
The point where the graph intersects the y-axis
What is the ‘x-intercept’ of a quadratic function?
The point(s) where the graph intersects the x-axis
What is the ‘domain’ of a quadratic function?
All real numbers
What is the ‘range’ of a quadratic function?
Depends on the value of ‘a’, typically y >= k for a > 0 and y <= k for a < 0
What is the ‘vertex’ of a quadratic function?
The highest or lowest point on the parabola
What is the ‘minimum’ of a quadratic function?
The lowest point on the parabola
What is the ‘maximum’ of a quadratic function?
The highest point on the parabola
What is the ‘root’ of a quadratic equation?
The solution(s) to the equation that make it true
What is the ‘discriminant test’ used for in quadratic equations?
To determine the number and nature of the roots of a quadratic equation
What is the ‘quadratic function’ of a quadratic equation?
A function of the form f(x) = ax^2 + bx + c
What is the ‘parabola’ of a quadratic equation?
The U-shaped graph of a quadratic function
