Quadratic Functions

What does the graph of a quadratic function look like?

• The graph is a straight line.

• The graph is a circle.

• The graph is a parabola that opens upwards if a > 0 and downwards if a < 0.

• The graph is a hyperbola.

What is the standard form of a quadratic function?

• y = ax² + bx + c

• y = a(x - h)² + k

• y = ax + b

• y = a/x + b

What does the discriminant tell us about the roots of a quadratic function?

• If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if it is negative, there are no real roots.

• If the discriminant is positive, there is one distinct real root; if it is zero, there are two real roots; if it is negative, there are no real roots.

• If the discriminant is positive, there are no real roots; if it is zero, there are two distinct real roots; if it is negative, there is one real root (a repeated root).

• If the discriminant is positive, there are two real roots; if it is zero, there are no real roots; if it is negative, there is one real root (a repeated root).

What is the range of a quadratic function that opens upwards?

• (-∞, k]

• [k, ∞)

• (k, ∞)

• [k, 0]

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 quadratic equation.

• The sum of the roots of the quadratic equation.

What is the significance of the coefficients a, b, and c in a quadratic function?

• The coefficient a determines the direction and width of the parabola, b affects the position of the vertex, and c represents the y-intercept.

• The coefficient a represents the y-intercept, b determines the direction of the parabola, and c affects the width.

• The coefficient a affects the width of the parabola, b represents the y-intercept, and c determines the direction.

• The coefficient a determines the position of the vertex, b represents the width, and c affects the direction of the parabola.

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 equation x = -b/(2a).

• A horizontal line that divides the parabola into two equal parts.

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

• The maximum or minimum point of the parabola.

What is the range of a quadratic function that opens downwards?

• (-∞, k] where k is the y-coordinate of the vertex

• [k, ∞) where k is the y-coordinate of the vertex

• (-∞, ∞)

• [k, 0] where k is the y-coordinate of the vertex

What is a quadratic function?

• A polynomial function of degree 1

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

• A linear function represented by y = mx + b

• A function that describes a straight line in a graph.

How do you find the vertex of a quadratic function in standard form?

• The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

• The vertex is always at the origin (0,0) of the graph.

• The vertex can be found by taking the average of the x-intercepts.

• The vertex is located at the maximum point of the graph only.