Quadratic Equations and Motion

These flashcards cover the key concepts of quadratic equations, their forms, the average rate of change, and applications in vertical motion problems.

What is the standard form of a quadratic equation?

f(x) = ax² + bx + c.

How does the direction of a parabola change depending on the value of 'a'?

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

What does the absolute value of 'a' determine in the graph of a parabola?

It determines the width of the parabola: if a > 1, it is narrower; if |a| < 1, it is wider.

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

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

What is the formula for finding the x-coordinate of the vertex in standard form?

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 vertex form?

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 do you find the average rate of change of a function over an interval?

Average rate of change = (f(b) - f(a)) / (b - a).

What is the standard formula for vertical motion?

h(t) = -16t² + V₁t + h₀, where V₁ is initial velocity and h₀ is initial height.

In a vertical motion problem, how do you determine the time until an object hits the ground?

Set h(t) to 0 and solve the equation for t.

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

Determine the x-coordinate of the vertex and plug it back into the function to find the y-coordinate.

What does the 'k' value represent in the vertex form of a quadratic equation?

The 'k' value is the constant term in the equation outside the parentheses.

How can you determine if the 'k' value represents a minimum or maximum?

If 'a' is positive (a > 0), 'k' is the minimum value; if 'a' is negative (a < 0), 'k' is the maximum value.