Quadratic Word Problems

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 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 a projectile 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 at a given time 't'.

Front

What does the term 'initial velocity' mean in projectile motion?

Back

Initial velocity is the speed at which an object is launched or starts moving, typically measured in feet per second (ft/s).

Front

What is the formula for the height of an object in free fall?

Back

The height of an object in free fall can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

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

Back

Set the height equation equal to zero (h(t) = 0) and solve for t to find the time when the object reaches the ground.

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

What is the axis of symmetry in a parabola?

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).