Quadratic Applications

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, indicating the values of x for which f(x) = 0.

Front

What does the y-intercept of a quadratic function indicate?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of the function when x = 0.

Front

How can you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by determining the y-value at the vertex of the quadratic function.

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h).

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

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

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

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, given by the equation x = h, where h is the x-coordinate of the vertex.