Quadratic Functions Word Problems

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 graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the quadratic equation ax² + bx + c.

Front

How do you find the maximum height of an object modeled by a quadratic function?

Back

To find the maximum height, determine the vertex of the parabola using x = -b/(2a) and then substitute this x-value back into the function to find the corresponding height.

Front

What is the significance of the 'h' in height equations?

Back

In height equations, 'h' represents the height of an object above the ground at a given time 't'.

Front

What does the 't' represent in height equations?

Back

In height equations, 't' represents time, usually measured in seconds.

Front

How do you determine when an object will hit the ground using a quadratic function?

Back

To determine when an object will hit the ground, set the height equation equal to zero and solve for 't'.

Front

What is the formula for the height of an object thrown upwards?

Back

The height of an object thrown upwards can be modeled by the equation h(t) = v₀t - ½gt², where v₀ is the initial velocity and g is the acceleration due to gravity.

Front

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

Back

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

Front

How do you find the time when a ball reaches its maximum height?

Back

The time when a ball reaches its maximum height can be found using the formula t = -b/(2a) from the quadratic equation.