2024 Week 1 Comparing Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is 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.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

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

Back

The vertex of a quadratic function in standard form f(x) = ax² + bx + c can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting back to find the y-coordinate.

Front

What does it mean for a parabola to be concave up?

Back

A parabola is concave up if it opens upwards, indicating that the vertex represents a minimum point of the function.

Front

What does it mean for a parabola to be concave down?

Back

A parabola is concave down if it opens downwards, indicating that the vertex represents a maximum point of the function.

Front

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

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

How can you determine the direction of a parabola?

Back

The direction of a parabola can be determined by the sign of the coefficient 'a' in the quadratic function f(x) = ax² + bx + c; if a > 0, it opens up, and if a < 0, it opens down.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex, given by the equation x = -b/(2a).

Front

How do you identify the minimum or maximum value of a quadratic function?

Back

The minimum or maximum value of a quadratic function occurs at the vertex; if the parabola opens upwards, it is a minimum, and if it opens downwards, it is a maximum.