exit tickets in solutions

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. For the function f(x) = ax^2 + bx + c, the vertex can be found using the formula: x = -b/(2a).

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (D = b^2 - 4ac). If D > 0, there are two solutions; if D = 0, there is one solution; if D < 0, there are no real solutions.

Front

What are the solutions, zeroes, roots, or x-intercepts of a quadratic function?

Back

These terms refer to the values of x where the graph of the function intersects the x-axis (f(x) = 0).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula: x = -b/(2a).

Front

What does it mean for a quadratic function to have a maximum or minimum?

Back

A maximum occurs when the parabola opens downwards (a < 0), and the vertex is the highest point. A minimum occurs when the parabola opens upwards (a > 0), and the vertex is the lowest point.

Front

Solve for x: f(x) = -x^2 - 4x + 12. What is the vertex?

Back

The vertex is (-2, 16).

Front

Solve: x^2 - 6x = 40. What are the solutions?

Back

The solutions are x = 10 and x = -4.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the solutions of the quadratic equation ax^2 + bx + c = 0.