Quadratic Applications - Characteristics

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 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 of the parabola.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

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

Front

How can you determine when an object launched upward will hit the ground using a quadratic equation?

Back

Set the height equation equal to zero and solve for t to find when the object hits the ground.

Front

What is the initial velocity in a quadratic height equation?

Back

The initial velocity is represented by the coefficient of the linear term (t) in the height equation, which indicates the speed at which the object is launched.

Front

What does the term 'positive zero' refer to in the context of quadratic applications?

Back

'Positive zero' refers to the positive x-intercept of the quadratic function, indicating the time when the object reaches the ground.

Front

How do you find the maximum height of an object thrown upward?

Back

The maximum height can be found by evaluating the function at the vertex, which gives the highest point of the parabola.

Front

What is the formula to calculate the time of flight for a projectile?

Back

The time of flight can be calculated by finding the positive root of the quadratic equation representing the height.