2/3 Quadratic Characteristics in Context

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 and a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola is the highest or lowest point of the graph, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the quadratic function.

Front

How can you determine the maximum height of a projectile using a quadratic function?

Back

The maximum height can be found by determining the vertex of the quadratic function, which occurs at x = -b/(2a) in the standard form.

Front

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

Back

The x-intercepts (or roots) of a quadratic function are the points where the graph intersects the x-axis, indicating the values of x for which the function equals zero.

Front

What does the term 'parabola' refer to in the context of quadratic functions?

Back

A parabola is the U-shaped graph of a quadratic function, which can open upwards or downwards depending on the sign of the leading coefficient (a).

Front

How do you find the time it takes for a projectile to land using a quadratic equation?

Back

To find the time it takes for a projectile to land, set the height (y) to zero in the quadratic equation and solve for x (time).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic function indicate about the graph?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How can you determine the height of a projectile at a specific time using a quadratic function?

Back

To determine the height at a specific time, substitute the time value into the quadratic function and solve for the height.

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 = -b/(2a).