Exploring Adding and Subtracting Rational Expressions

What are the different terms used to describe the solutions of a quadratic equation?

• Coefficients, terms, constants

• Factors, divisors, products

• Vertices, nodes, edges

• Zeros, roots, x-intercepts

How many solutions does a parabola have if its vertex lies on the x-axis?

• Two solutions

• No solutions

• One solution

• Infinite solutions

What is the formula used to find the vertex of a parabola in standard form?

• x = b / 2a

• x = -b / 2a

• x = 2a / b

• x = -2a / b

What does the vertex represent in the graph of a quadratic equation?

• The point where the graph crosses the x-axis

• The intersection point with the y-axis

• The highest or lowest point on the parabola

• The point where the graph is widest

What are the x-intercepts of the quadratic equation if the parabola touches the x-axis at two distinct points?

• The points where x equals zero

• The points where y equals zero

• The vertex points

• The focus points

How do you determine the number of solutions a quadratic equation has by graphing?

• By locating the vertex on the y-axis

• By determining the width of the parabola

• By finding the maximum height of the parabola

• By counting the number of times it crosses the x-axis

What does a negative coefficient on the x^2 term indicate about the parabola's shape?

• It opens downwards

• It is wider than usual

• It opens upwards

• It is narrower than usual

What is the axis of symmetry in the context of a parabola?

• The line along which the parabola is widest

• A vertical line that divides the parabola into two symmetrical halves

• A horizontal line that divides the parabola into two symmetrical halves

• The line along which the parabola is narrowest

What notation is used to indicate no real solutions in set notation?

• Empty set

• Zero set

• Universal set

• Single-element set

If a quadratic equation's graph does not intersect the x-axis, how many real solutions does it have?

• Two

• Infinite

• One

• None