Quadratic Applications

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 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

For a quadratic function in standard form y = ax² + bx + c, the vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

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

Back

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

Front

What is the formula for the maximum height of a projectile given its initial velocity and height?

Back

The maximum height can be found using the formula h = -b²/(4a) + c, where h is the maximum height, and the quadratic function is in the form h(t) = at² + bt + c.

Front

What does it mean for a quadratic function to have a negative leading coefficient?

Back

If a quadratic function has a negative leading coefficient (a < 0), the parabola opens downwards, indicating that it has a maximum point.

Front

How can you determine the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

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

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = -b/(2a).