Introduction to Quadratic Functions

What is the discriminant in a quadratic equation?

• The coefficient of the linear term in the equation.

• The part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

• The constant term in the equation.

• The sum of the roots of the equation.

What does a positive discriminant indicate?

• There are no real roots.

• There is one real root.

• There are two distinct real roots.

• The roots are complex conjugates.

What does a zero discriminant indicate?

• There are two distinct real roots.

• There is exactly one real root (the vertex touches the x-axis).

• There are no real roots, only complex roots.

• The roots are imaginary and cannot be calculated.

What is a quadratic function?

• A polynomial function of degree 1, typically in the form f(x) = ax + b, where a ≠ 0.

• A polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

• A polynomial function of degree 3, typically in the form f(x) = ax³ + bx² + cx + d, where a ≠ 0.

• A linear function represented by a straight line, typically in the form f(x) = mx + b.

What is the standard form of a quadratic function?

• f(x) = ax² + bx + c

• f(x) = a(x - h)² + k

• f(x) = a(x + b)(x - c)

• f(x) = ax³ + bx² + cx + d

What are the roots of a quadratic equation?

• The values of x that make the quadratic equation equal to zero; they are the x-intercepts of the graph.

• The coefficients of the quadratic equation that determine its shape.

• The maximum or minimum points of the quadratic function.

• The points where the graph intersects the y-axis.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The highest or lowest point of the parabola, depending on its direction of opening.

• The distance from the vertex to the focus of the parabola.

• The line that divides the parabola into two symmetrical halves.

What is the axis of symmetry in a quadratic function?

• A vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

• A horizontal line that intersects the vertex of the parabola.

• The point where the parabola touches the x-axis.

• The maximum or minimum point of the parabola.

How do you determine the direction of the opening of a parabola from its equation?

• By looking at the coefficient 'a': if 'a' is positive, it opens upward; if 'a' is negative, it opens downward.

• By checking the value of 'b' in the equation of the parabola.

• By analyzing the vertex of the parabola only.

• By determining the x-intercepts of the parabola.

What is the significance of the y-intercept in a quadratic function?

• The y-intercept is the point where the graph intersects the x-axis.

• The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0) = c.

• The y-intercept represents the maximum value of the function.

• The y-intercept indicates the slope of the function.