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