#1
What is the general form of a quadratic equation?
ax^2 + bx + c = 0
ExplanationStandard form of a quadratic equation.
#2
How many solutions can a quadratic equation have?
Two
ExplanationQuadratic equations generally have two solutions.
#3
What is the sum of the roots of a quadratic equation of the form ax^2 + bx + c = 0?
-b/a
ExplanationSum of roots equals negative b over a.
#4
What is the standard form of a quadratic equation?
ax^2 + bx + c = 0
ExplanationStandard form of quadratic equation.
#5
What is the quadratic formula used for?
Finding the roots of a quadratic equation
ExplanationQuadratic formula finds equation's roots.
#6
What is the axis of symmetry of a parabola given by the equation y = ax^2 + bx + c?
x = -b/2a
ExplanationLine through vertex, divides parabola into two symmetrical halves.
#7
Which method is commonly used to solve quadratic equations?
Factoring
ExplanationCommon method for solving quadratic equations.
#8
What is the discriminant of a quadratic equation used for?
To determine the number of real solutions
ExplanationDiscriminant helps identify the nature of roots.
#9
What is the relationship between the roots and coefficients of a quadratic equation?
Roots are directly proportional to coefficients
ExplanationRelationship between roots and coefficients.
#10
Which formula is used to find the roots of a quadratic equation when the coefficients are given?
Quadratic formula
ExplanationFormula for finding roots of quadratic equations.
#11
Which method is suitable for solving quadratic equations that cannot be easily factored?
Completing the square
ExplanationMethod for solving difficult quadratic equations.
#12
Which property allows you to factor a quadratic equation as (x - r)(x - s) if r and s are the roots?
Zero-product property
ExplanationProperty used for factoring quadratic equations.
#13
In the quadratic formula, what does '±' represent?
Plus or minus
ExplanationIndicates two possible solutions.
#14
If a quadratic equation has no real roots, what can be said about its discriminant?
Discriminant is negative
ExplanationDiscriminant is negative for no real roots.
#15
If a quadratic equation has one real root, what can be said about its discriminant?
Discriminant is zero
ExplanationDiscriminant equals zero for one real root.
#16
If a quadratic equation has two complex conjugate roots, what can be said about its discriminant?
Discriminant is negative
ExplanationDiscriminant is negative for complex roots.
#17
What is the relationship between the vertex form and the standard form of a quadratic equation?
They are equivalent
ExplanationVertex form and standard form have same solutions.
#18
If a quadratic equation has no real roots, what can be said about its graph?
The graph does not touch the x-axis
ExplanationGraph does not intersect the x-axis.