Applications of Quadratics

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 does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, indicating a minimum point.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is negative, indicating a maximum point.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form f(x) = ax² + bx + c can be found using the formula x = -b/(2a).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens downwards or upwards.

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).

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by evaluating the quadratic function at the vertex, which gives the highest point the projectile reaches.

Front

How do you determine the time it takes for an object to hit the ground using a quadratic equation?

Back

Set the height equation equal to zero and solve for t to find the time when the object reaches ground level.

Front

What does the y-axis represent in a projectile motion graph?

Back

In a projectile motion graph, the y-axis typically represents the height of the object from the ground.