Applications with Quadratics

Front

What is the general form of a quadratic equation?

Back

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

Front

What does the variable 'h' represent in the equation h = -16t² + 320?

Back

In this equation, 'h' represents the height of the object above the ground at time 't'.

Front

How do 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 't' to find when the object reaches the ground.

Front

What is the significance of the coefficient -16 in the height equations?

Back

The coefficient -16 represents the acceleration due to gravity in feet per second squared, affecting the object's height over time.

Front

How can you find the maximum height of a projectile modeled by a quadratic equation?

Back

The maximum height can be found by calculating the vertex of the parabola, which occurs at t = -b/(2a) in the equation h = at² + bt + c.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

Initial velocity refers to the speed and direction at which an object is thrown or dropped at the start of its motion.

Front

How do you calculate the height of an object at a specific time using a quadratic equation?

Back

Substitute the specific time value into the height equation and solve for 'h'.

Front

What is the formula to find the time at which a projectile reaches its maximum height?

Back

The time to reach maximum height is given by t = -b/(2a) from the quadratic equation h = at² + bt + c.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.