Quadratic Applications :-)

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the y-intercept represent in a quadratic function?

Back

The y-intercept represents the initial value of the function when the independent variable (usually time) is zero.

Front

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

Back

To find the maximum height, use the vertex formula t = -b/(2a) to find the time at which the maximum occurs, then substitute this time back into the height equation.

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward or downward), 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

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

Back

Set the height equation equal to zero and solve for the time variable t.

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

What does the vertex of a parabola represent in the context of projectile motion?

Back

The vertex represents the maximum height of the projectile and the time at which it occurs.

Front

How do you interpret the roots of a quadratic equation in a real-world context?

Back

The roots of a quadratic equation represent the points in time when the object is at ground level (height = 0).

Front

What is the role of gravity in the equations of motion for projectiles?

Back

Gravity affects the vertical motion of projectiles, typically represented by the coefficient of t² in the height equation, which is -16 in feet per second squared.

Front

What is the initial height of an object if the quadratic equation is h(t) = -16t² + 20t + 6?

Back

The initial height is the constant term, which is 6 feet.