Key Features of Quadratics Explained

What is the primary characteristic of a quadratic equation?

• It cannot have complex roots.

• It is always solvable by factoring.

• It is linear in nature.

• It always includes an x squared term.

What role does the 'c' term play in a quadratic equation?

• It determines the y-intercept.

• It affects the direction of the parabola.

• It changes the vertex position.

• It indicates the number of roots.

What does the coefficient 'a' in a quadratic equation influence?

• The x-intercepts of the graph.

• The direction of the parabola's opening.

• The linearity of the equation.

• The y-intercept only.

What is the significance of the 'b' coefficient in the standard form of a quadratic equation?

• It influences the vertex's x-coordinate.

• It determines the symmetry of the parabola.

• It sets the initial rate of change.

• It modifies the quadratic's width.

What is the vertex of a parabola?

• The slope of the tangent at any point.

• The coefficient of x squared.

• The highest or lowest point on the graph.

• The point where it crosses the y-axis.

What is the axis of symmetry in a parabola?

• The rate of change of the quadratic.

• The maximum height of the parabola.

• A vertical line through the vertex.

• The point where it intersects the x-axis.

What does the vertex represent in the context of a parabola's graph?

• The point of maximum curvature.

• The intersection point with the y-axis.

• The average rate of change.

• The turning point of the graph.

How does a negative 'a' value affect a parabola?

• It opens downwards.

• It eliminates real roots.

• It makes the parabola linear.

• It shifts the graph to the right.

How can you determine the orientation of a parabola from its equation?

• By the constant term.

• By the coefficient of x.

• By the highest degree of x.

• By the sign of the coefficient 'a'.

What are the x-intercepts of a quadratic known as?

• Solutions

• Vertices

• Coefficients

• Constants