Alg 2 Quadratic Applications

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

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form can be found using the formula x = -b/(2a). The y-coordinate can be found by substituting x back into the function.

Front

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

Back

The x-intercept represents the points where the graph of the quadratic function crosses the x-axis, indicating the values of x for which the function equals zero.

Front

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

Back

The y-coordinate of the vertex represents the maximum or minimum value of the quadratic function, depending on the direction of the parabola.

Front

How can you determine the maximum height of an object modeled by a quadratic equation?

Back

To determine the maximum height, find the y-coordinate of the vertex using the formula y = -b²/(4a) + c.

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 term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots, indicating that the graph does not intersect the x-axis.