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).

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.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola.

Front

What does the 'b' value in a quadratic equation represent?

Back

The 'b' value affects the position of the vertex along the x-axis and influences the slope of the parabola.

Front

What does the 'c' value in a quadratic equation represent?

Back

The 'c' value represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

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

Back

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

Front

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

Back

The height 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 calculate the time to reach maximum height for a projectile?

Back

The time to reach maximum height is found using t = -b/(2a) from the quadratic equation.