Quadratics in Context In Class Practice

Front

What is the y-intercept of 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 vertex of a quadratic function represent?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its orientation.

Front

How do you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found at the vertex of the parabola, which can be calculated using the formula t = -b/(2a) for the function h(t) = at^2 + bt + c.

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

What does it mean if a quadratic equation has two solutions?

Back

It means the graph of the quadratic function intersects the x-axis at two points.

Front

What does it mean if a quadratic equation has one solution?

Back

It means the graph of the quadratic function touches the x-axis at exactly one point (the vertex) and does not cross it.

Front

What does it mean if a quadratic equation has no solutions?

Back

It means the graph of the quadratic function does not intersect the x-axis at all, indicating that the parabola is entirely above or below the x-axis.

Front

How can you determine the time it takes for a projectile to reach its maximum height?

Back

The time to reach maximum height can be found using the formula t = -b/(2a) from the quadratic function h(t) = at^2 + bt + c.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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