Quadratic Equations and Motion

These flashcards cover key concepts related to quadratic equations, including standard and vertex forms, characteristics of parabolas, and vertical motion.

What is the standard form of a quadratic equation?

f(x) = ax² + bx + c.

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

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

What does the constant 'c' represent in the standard form of a quadratic equation?

The constant 'c' is the y-intercept of the graph.

How is the vertex of a parabola found in standard form?

The x-coordinate of the vertex can be found using the formula x = -b/2a.

What is the vertex form of a quadratic equation?

f(x) = a(x − h)² + k.

What does the point (h, k) represent in the vertex form of a quadratic equation?

The vertex of the parabola.

What is the axis of symmetry in the vertex form of a quadratic equation?

The axis of symmetry is the vertical line x = h.

How is the average rate of change calculated from a function?

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

What is the standard formula for vertical motion?

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

How do you find max/min values from standard form of a parabola?

Determine the direction of the parabola, find the vertex, and calculate the maximum/minimum value using the original function.

How do you find max/min values from vertex form of a parabola?

Identify the 'k' value and check the coefficient 'a' to determine if it's a minimum or maximum.

If 'a' in the vertex form is positive, what value does 'k' represent?

'k' is the minimum value.

If 'a' in the vertex form is negative, what value does 'k' represent?

'k' is the maximum value.