Quadratic 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 of a parabola is the highest or lowest point on the graph, depending on the direction it opens. 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 coefficients in a quadratic function?

Back

In the quadratic function f(x) = ax² + bx + c, 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

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

Back

To determine when an object hits the ground, set the height function equal to zero and solve for the variable (usually time).

Front

What is the formula for the height of an object in projectile motion?

Back

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

Front

What does the term 'initial height' refer to in projectile motion?

Back

The initial height is the height from which the object is launched or dropped, represented by h₀ in the height equation.

Front

What is the role of gravity in quadratic motion equations?

Back

Gravity affects the vertical motion of an object, typically represented by the coefficient of the t² term in the quadratic equation, which is negative due to the downward acceleration.

Front

How can you find the time at which an object reaches its maximum height?

Back

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