Quadratic applications

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

How do you find the time at which a projectile reaches maximum height?

Back

To find the time at which a projectile reaches maximum height, use the formula t = -b/(2a) from the vertex form of the quadratic equation.

Front

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

Back

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

Front

How can you determine when a projectile hits the ground using a quadratic equation?

Back

Set the quadratic equation equal to zero and solve for the variable to find the time when the height is zero.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax² + bx + c = 0.

Front

What does the coefficient 'a' indicate in a quadratic function?

Back

The coefficient 'a' indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula to find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function can be found using the formula f(-b/(2a)).

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).

Front

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

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.