Quadratic Functions and Motion

These flashcards cover key concepts related to quadratic functions, including their forms, properties, and applications in motion problems.

What is the standard form of a quadratic equation?

f(x) = ax² + bx + c

How does the sign of 'a' affect the direction of a parabola?

If a > 0, the parabola opens upward; if a < 0, it opens downward.

What does the absolute value of 'a' indicate about the width of a parabola?

If a > 1, the parabola is narrower; if |a| < 1, it is wider.

In the standard form of a quadratic equation, what does the constant 'c' represent?

The y-intercept of the graph.

How do you find the x-coordinate of the vertex in standard form?

Using the formula x = -b/(2a).

What is the vertex form of a quadratic equation?

f(x) = a(x − h)² + k.

What is the vertex of the parabola in vertex form?

The point (h, k).

What is the axis of symmetry in vertex form?

The vertical line x = h.

How do you calculate the average rate of change of a function?

Average rate of change = (f(b) - f(a)) / (b - a) for the interval [a, b].

What is the standard formula for vertical motion?

h(t) = -16t² + V₀t + h₀, where V₀ is initial velocity and h₀ is initial height.

In vertical motion problems, what does h(t) represent?

The height of the object at time t.

How can you find the maximum or minimum value of a parabola in standard form?

Calculate the vertex and substitute the x-coordinate into the function to find the y-coordinate.

What does the 'k' value represent in vertex form?

The maximum or minimum value of the parabola.

How do you determine if the 'k' value is a maximum or minimum in vertex form?

If 'a' is positive, 'k' is minimum; if 'a' is negative, 'k' is maximum.