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 vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction the parabola opens.

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found using the vertex formula: x = -b/(2a). Substitute this x-value back into the function to find the corresponding y-value.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

How can you determine the time an object reaches the ground using a quadratic function?

Back

Set the height function h(t) equal to zero and solve for t to find when the object hits the ground.

Front

What does the coefficient of x² indicate about the parabola's direction?

Back

If the coefficient of x² (a) is positive, the parabola opens upwards; if it is negative, the parabola opens downwards.

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) = -gt² + v₀t + h₀, where g is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height.

Front

How do you find the time of flight for a projectile?

Back

The time of flight can be found by determining when the height function equals zero and solving for t.

Front

What is the maximum height of a projectile?

Back

The maximum height can be found by calculating the vertex of the height function, using the formula h = -b²/(4a) for the height at the vertex.