Quadratic Applications :-)

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, 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 (opening upwards or downwards).

Front

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

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

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, found by evaluating f(0).

Front

What is the formula for the height of an object in free fall?

Back

The height h of an object in free fall can be modeled by the equation h = -16t² + h₀, where h₀ is the initial height and t is time in seconds.

Front

How do you determine the maximum height of a projectile modeled by a quadratic equation?

Back

The maximum height can be found by calculating the vertex of the quadratic equation, specifically the y-coordinate of the vertex.

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 of the equation.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation are the x-values where the graph intersects the x-axis; they can be real or complex depending on the discriminant.

Front

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

Back

Set the height equation to zero and solve for t to find the time when the object reaches the ground.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).