Quadratic Functions Review

What does a positive discriminant indicate?

• There are no real roots.

• There is one real root.

• There are two distinct real roots.

• There are infinitely many roots.

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 does a negative discriminant indicate?

• There are two distinct real roots (the parabola intersects the x-axis at two points).

• There is one real root (the parabola touches the x-axis at one point).

• There are no real roots (the parabola does not intersect the x-axis).

• The roots are complex and conjugate pairs.

What is the standard form of a quadratic function?

• y = ax + b

• y = ax² + bx + c

• y = a/x + b

• y = ax² - bx + c

What is the axis of symmetry in a parabola?

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

• A vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

• A diagonal line that intersects the parabola at two points.

• A line that is tangent to the parabola at its vertex.

What is the vertex form of a quadratic function?

• y = a(x-h)² + k, where (h, k) is the vertex.

• y = ax² + bx + c, where a, b, and c are constants.

• y = a(x + h)² + k, where (h, k) is the vertex.

• y = a(x - h)² - k, where (h, k) is the vertex.

What does a zero discriminant indicate?

• There are no real roots.

• There are two distinct real roots.

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

• There are infinitely many real roots.

What is a quadratic function?

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

• A linear function represented by a straight line on a graph.

• A function that has a constant rate of change.

• A polynomial function of degree 3, typically in the form y = ax³ + bx² + cx + d.

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

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

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

• The vertex can be found by taking the square root of the leading coefficient.

• The vertex is located at the point 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 on the graph, depending on the direction it opens.

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

• The midpoint of the line segment connecting the focus and directrix.