Understanding Quadratic Functions and Equations

What is the shape of the graph of a quadratic function?

• Ellipse

• Hyperbola

• Parabola

• Circle

How many x-intercepts does the function 'x-squared' have?

• Two

• One

• Three

• None

What are the x-intercepts of the function 'x-squared - 4'?

• 0 and 4

• 4 and -4

• 2 and -2

• 1 and -1

What type of numbers were introduced to handle functions with no real roots?

• Prime numbers

• Rational numbers

• Imaginary numbers

• Whole numbers

How many roots do all quadratic functions have when considering complex numbers?

• Four

• Three

• Two

• One

What property is used to solve quadratic equations by factoring?

• Distributive property

• Associative property

• Zero product property

• Commutative property

What must be true for a product of factors to be zero?

• All factors must be non-zero

• At least one factor must be zero

• The product must be positive

• The product must be negative

Is it always possible to factor a quadratic function into linear functions if its graph intersects the x-axis?

• Only if it has one intersection point

• No

• Yes

• Only if it has two intersection points

What is a 'difference of squares' in quadratic expressions?

• A quadratic expression that is the difference between two squared terms

• A quadratic expression that can be factored into two distinct linear expressions

• A quadratic expression that can be factored into two identical linear expressions

• A quadratic expression with no real roots

What are 'perfect squares' in the context of quadratic expressions?

• Expressions that are the square of a binomial

• Expressions with no x-intercepts

• Expressions that cannot be factored

• Expressions with complex roots