Quadratic Equation Flashcards
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0.
True or False: The standard form of a quadratic equation is y = ax² + bx + c.
True.
Fill in the blank: The values of a, b, and c in a quadratic equation ax² + bx + c = 0 are called _____ coefficients.
constant.
What is the vertex of a quadratic function?
The vertex is the highest or lowest point on the graph of a quadratic function.
Multiple choice: Which formula is used to find the roots of a quadratic equation?
The quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
What does the discriminant (b² - 4ac) indicate?
The discriminant indicates the nature of the roots of the quadratic equation.
True or False: If the discriminant is positive, the quadratic equation has two distinct real roots.
True.
What is the axis of symmetry in a quadratic equation?
The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).
Fill in the blank: A quadratic equation can have _____ real roots.
zero, one, or two.
Multiple choice: What is the shape of the graph of a quadratic function?
A parabola.
What is the formula for the vertex of a quadratic equation in standard form?
The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).
True or False: A quadratic equation can be factored if the roots are rational.
True.
What is the general form of a quadratic equation?
The general form is ax² + bx + c = 0 where a ≠ 0.
Fill in the blank: The graph of a quadratic equation opens _____ if the coefficient a is positive.
upward.
Multiple choice: If a = 0 in a quadratic equation, what type of equation is it?
It is not a quadratic equation; it is a linear equation.
What is the y-intercept of a quadratic function?
The y-intercept is the point where the graph crosses the y-axis, given by c in the equation y = ax² + bx + c.
True or False: Completing the square is a method to solve quadratic equations.
True.
What are the steps to complete the square for a quadratic equation?
- Move the constant to the other side. 2. Divide by a. 3. Add (b/2)² to both sides. 4. Factor the left side.
Fill in the blank: The roots of a quadratic equation can also be found by _____.
graphing.
Multiple choice: Which of the following is an example of a quadratic equation?
x² - 5x + 6 = 0.
What is the relationship between the coefficients and the roots in a quadratic equation?
The sum of the roots is -b/a and the product of the roots is c/a.
True or False: The graph of a quadratic function can be symmetric about the y-axis.
False; it is symmetric about the axis of symmetry.
What is the maximum or minimum value of a quadratic function?
It occurs at the vertex and can be found by evaluating f(h) where h = -b/(2a).
Fill in the blank: A quadratic equation can be expressed in _____ form, vertex form, and factored form.
standard.
Multiple choice: Which method is NOT typically used to solve quadratic equations?
Graphing is not a method in strict algebraic terms, though it is a visual technique.
